Abstract: Load management programs were initiated in the 1970s to actively influence customer demand. Using the load management programs to minimize operating cost or to improve system reliability is suitable when utilities are regulated. However, these objectives may no be suitable for companies competing in a competitive environment. In this paper, various economic objectives of the load management programs are evaluated and compared. These include load-based objective that minimizes peak demand, cost-based objective that minimizes operating cost, profit-based objective that maximizes the profit of serving customer energy, and cash management objective that maximizes cash flow. The gaps between cost-based objective and profit-based objective are discussed. Finally, this paper suggests why the dilemma faced by the load management programs in a regulated power industry should not be a concern in a deregulated power industry, assuming that deregulation is to promote competitions.
Keywords: load management programs, economics, deregulation, direct load control (DLC), indirect load control (IDLC), energy storage system (ESS).
I. INTRODUCTION
Calls for competition in the power industry, from the wholesale to the retail level, has made deregulation an attractive option around the world. A study of this new evolving market structure reveals the need for a more acceptable framework that would ultimately satisfy regulatory bodies, customers, and suppliers, alike. One approach is the application of a brokerage system to the power industry to promote competition. To accomplish this, existing vertically integrated utilities need to be broken up. The framework of an energy market can be found in [1].
The deregulation in the power industry provides many research opportunities. One of these opportunities is studying how the regulated power industry should re-strategize itself to operate in a deregulated, competitive environment. In this paper, load management programs are evaluated. In particular, this paper emphasizes on the economics of load management programs, should the programs be adopted by the deregulated power industry.
In section II, load management programs prior to deregulation are investigated. Section III presents various economic models of load management programs. The differences among various economic models are reviewed in section IV. Section V provides an example comparing the various economic objectives of load management programs. Section VI identifies òthe gaps between cost-based and profit-based load management programs. An example is also included to compare the two economic objectives. Section VI examines the future perspectives of the load management programs in a deregulated energy market. Finally, section VIII concludes this paper, emphasizing that load management programs should be evaluated in the deregulated energy market based on the economic advantages that the programs can provide.
II. LOAD MANAGEMENT PROGRAMS: PRIOR TO DEREGULATION
Generally, load management programs can be categorized into direct load control (DLC), indirect load control (IDLC), and energy storage system (ESS). The DLC allows the utilities to shed remote customer demand unilaterally. IDLC allows the customers to control their demand independently according to the price signals sent by the utilities serving the energy services. Both DLC and IDLC share the same concept, where controllable demands are shifted to the future where the economic values are higher. However, they differ on who has the ultimate control on the electric appliances. Finally, ESS allows both the utilities and the customers to store energy during low-cost sessions and consume during high-cost sessions. References [2,3] are among all work reporting on the technological development of load management programs.
There are two commonly recognized economic objectives of load management programs in the regulated power industry. The first is to minimize the costs of operation. These costs include the cost of energy, cost of transmission losses and cost of reliability. The second is to minimize the peak demand to improve the reliability of the transmission systems. Algorithms developed for the load management programs to achieve the two reported economic objectives have been reported. Some of these algorithms can be found in [4 – 19].
Since its inception, the demand under the load management programs has accounted for 5% to 10% of the total electric demand. The programs once flourished in the early 1980s. However, as time went on, interest in the program subsided. Except in states like Florida and California, with insufficient generating capacity to handle the peak demand, the programs are generally not a popular option anymore. The lack of interest in the programs is attributable to three major reasons. First, the load management programs are relatively young compared to the power industry in general. The technology has not matured enough for the utilities to feel comfortable about adopting the load management programs. Second, to a large degree, the load management programs are regulatory forced upon the utilities. Utilities may not see the value of the programs but still adopt them to please the regulators. With no proper incentive, the growth in adopting the programs is naturally slowed. Finally, the load management programs can be used by the utilities as a shortcut to cross subsidize some customers. Or, as Andrew Rudin put it, “the program unfairly taxes non-participants” [20]. Thus, the economic benefits of load management programs are not fully realized.
III. ECONOMICS OF LOAD MANAGEMENT PROGRAMS
In this section, economic models of load management programs, particularly DLC and ESS, are presented. These include the cost-based objective that minimizes peak demand, cost-based objective that minimizes operating cost, profit-based objective that maximizes the profit of serving customer energy, and cash management objective that maximizes cash flow. For simplicity, only the cost of energy is considered in this section.
When DLC and ESS are introduced, the
energy to be generated, 
, at period j is
shown in (1).
(1)
is the total customer
demand at period j, 
is the deferred DLC
demand at period j, 
is the paid back DLC
demand at period j, 
is the energy stored
at period j, and 
is the energy
released from the ESS at period j. The models for 
, 
, 
, and 
can be found in [23].
The load-based model, shown in (2), minimizes the maximum energy to be generated.
(2)
E is the maximum
periodic energy to be generated; 
is described in (1).
Prior to the introduction of load
management programs, total customer demand is served at a per-unit energy cost
of 
. The cost of serving
customer demands with the load management programs is 
. The cost-based
model, shown in (3), minimizes the increased cost of load management.
(3)
is the rebate given
to the customers participating in the DLC program at period j and 
is the operating cost
of ESS at period j.
With
DLC and ESS implemented, the cost of purchased energy is 
. The collectible
revenue, 
, at period j is
shown in (4).
(4)
Any stored energy at period j, 
, does not generate revenue, and any released energy at
period j, 
, contributes toward the inflow of revenue.
The profit of serving customer demand after the implementation of the load management programs at period j is shown in (5).
(5)
The profit-based model, shown in (6) maximizes the gain from the load management programs.
(6)
Utilities receive payments from the customers periodically for the energy served. Meanwhile, they must make payments to generate energy and to pay for operating and maintenance costs. At the end of each day, utilities have to decide if they have enough cash on hand to pay for tomorrow’s expenses. If the utilities should choose to raising funds, they have to determine when and how to raise that capital. Also, it must decide the expiration date for each type of capital raised. Likewise, if the utilities should choose to invest the excess cash, it has to determine when and how to invest it. Also, it has to decide the maturity date of each investment.
A generic cash management model that maximizes the cash buildup at the end of the considered duration can be found in [22]. The cash management model includes the impacts of the cost of raising capital and the cost of investing excess capital. A cash management model that considers the impact of load management programs in serving customer electric energy can be found in [21].
IV. COMPARING THE VARIOUS ECONOMIC MODELS
The four economic models that consider the impact of load management programs differ by what were included in the objective function. The load-based model is the simplest of all. It attempts to reduce the peak demand. The cost-based model advances the load-based model to include the cost of energy. Even though the cost-based model does not specifically reduce the peak demand, it does implicitly carrying out the task. The cost of energy, more often than not, depends on the supply and demand of energy. As energy demand increases, the cost of energy will usually increase to reflect the higher cost of production. Thus, even though the cost-based model does not explicitly reduce the peak demand, it will usually lead to peak reduction, but less dramatically.
There are, in general, two ways that the revenue could change. First, when DLC energy is deferred to a low-rate period from a high-rate period (or vice-versa,) the utilities experience a reduction (increase) in the revenue due to a difference in the rate over time. Second, when paid back DLC energy is lower (higher) than the deferred energy, the utilities experience a reduction (increase) in the revenue due to changes in the customer demand or energy loss. Using a simple, two-period example, [23] shows that a cost-based economic model and a profit-based economic model differ only on the degree of implementation, i.e., a profit-based model considers the impact of the potential change in revenue while a cost-based model does not coònsider such impact. If proper discount factors are included in the economic models to reflect the load management programs’ impact on revenue, a cost-based model will be equivalent to a profit-based model.
Since a cost-based model implicitly reduces the peak demand and the difference between a cost-based model and a profit-based model is on the potential change in revenue, a profit-based model will also implicitly reduce the peak demand. However, since the profit-based model includes the potential change in the revenue to the objective function, the model will prevent the scheduling of customer demand from hurting the utilities’ profit more than the cost-based model.
Even though the model seems complicated, the cash management model differs from the profit-based model only in terms of implied cash flow. The inclusion of the cost of borrowing and lending guards the utilities against excessive lending and borrowing. It also makes the utilities aware of the cost of borrowing. Thus, a profit-based model that does not include the cost of lending and borrowing in the objective function may improve the profitability in the short-run, but hurt the utilities’ performance in the long run. Table 1 shows the different models and their effects on peak demand, cost, revenue, and cash flow.
Since the cash management model includes most factors in the scheduling model, one may incline to suggest the cash management model as the best economic model for load management programs. However, a careful study of the different models may suggest otherwise.
In
the cash management model, energy cost is included in the constraining
equations. Nonlinear energy cost functions
will cause the constraining equations in the cash management model to be
nonlinear as well. This will pose
difficulty in solving the scheduling problem using a cash management model in
the short time. In addition, the number
of variables also increases tremendously to reflect the opportunity to loan and
invest, making the cash management model harder to use than any other
model. In evaluating the utilities’
operation for a time horizon shorter than one month, the costs of borrowing and
investing are not significant factors.
Thus, in the short-run, a profit-based model that uses less variables
can be more effective (time-wise). When
evaluating the utilities’ operation in the longer run, the cash management
model becomes more important, as the cost impact of borrowing and lending
becomes significant.
Table 1. Scheduling customer demand and its effect.
|
Factoring in |
||||
|
Peak demand |
Cost |
Revenue |
Cash flow |
|
|
Load-based |
Ö |
Implied |
´ |
´ |
|
Cost-based |
Implied |
Ö |
´ |
´ |
|
Profit-based |
Implied |
Ö |
Ö |
´ |
|
òCash management |
Implied |
Ö |
Ö |
Ö |
V. AN EXAMPLE COMPARING THE VARIOUS ECONOMIC OBJECTIVES
In this section, an example is presented to compare the various economic models. In this example, it is assumed that there are six periods in one day and one day in each month. Also, a company serving customers energy has two groups of customers participating in the DLC program. It does not have any ESS or any customer participating in the IDLC programs. The company will pay the cost of generating electric energy during a day at the end of the day. However, the company will receive payments from the customers for the energy served during a day only at the beginning of next month. Six months of customer data, DLC demand data, and per unit energy costs are shown in [21].
Table 2 compares the results of scheduling the controllable customer demand using the load management programs. Since the company has to borrow to pay for the energy cost at the end of each day, while waiting for the customers to pay the cost of services at the beginning of the next month, the cash buildup is in general lower than the profit. All economic models result in a lower cost for energy and a higher profit of serving customer energy. Since the rate offered to customers is higher during peak periods and some customer demand is deferred during peak periods, the load management programs result in lower revenue.
Under the load-based model, even though the peak demand is the lowest after scheduling, the peak demands during the various months are not always the lowest. For example, in the 1st month, the peak demand is the lowest under the cost-based model at 65.70MW. However, during the same duration, the peak demand is higher at 68MW under the load-based model. This is because the objective of a load-based model minimizes the highest peak demand during the 6 months duration, which has a peak demand of 77MW in the 6th month. With this peak demand minimized to 74.91MW, the load-based model has achieved its goal. Thus, the formulated load-based model should be modified when there is multiple peak demand during the schedule duration.
Since a cost-based model does not consider the impact of lowered revenue when the controllable demand during peak periods is deferred to off-peak periods, and when the paid back energy is lower than the deferred energy, the collected revenue under this model is the lowest among all. Thus, even though the load-based model results in the lowest cost of energy, this model does not guarantee the highest profit.
A profit-based model results in the highest profit, even òwhen the cost of energy is not the lowest. By considering the impact of lowered revenue, this model makes sure that only when the cost savings exceed the lowered revenue will energy deferment be conducted. In section VI, the cost-based model and profit-based model are further investigated.
Even though the profit reached is the highest, the profit-òbased model does not guarantee the highest cash flows. In this example, the company will receive the revenue at the beginning of the 3rd month after the energy is served. However, the company has to pay the energy cost at the end of each day. Any cost saving made today has a higher impact than the lowered revenue. Thus, the cash management model that includes the impact of interest payment results in higher cash flows than the profit-based model.
In this example, there is only six periods in each day, and one day in each month. Therefore, the cost savings, increased profits, and customer benefits are relatively small. In addition, in this example, the impact of congestion cost is not considered. Thus, the energy prices during peak periods are not significantly higher than during off-peak periods (less than 20%). As a result, the benefits of the load management programs are not yet fully realized.
VI. THE GAPS BETWEEN COST-BASED OBJECTIVE AND PROFIT-BASED OBJECTIVE
There are four potential changes in collectible revenue when DLC demand is deferred. They are
1. revenue loss due to reduced DLC demand during pay back or cold load pickup – RLD.
2. revenue loss due to reduced rate charged on customers during the pay back (rate structure during energy deferment is higher than the rate structure during energy pay back.) – RLR.
3. revenue increase due to higher DLC demand during pay back or cold load pickup – RID.
4. revenue increase due to higher rate charged on customers during the pay back(rate structure during energy deferment is lower than the rate structure during energy pay back.) – RIR.
The models that include the potential changes in the collectible revenue can be found in [21]. Table 3 shows the results after including remedies (RLD, RLR, RID, and RIR) into the cost-based model and profit-based model in section III for the company in section V.
Results show that, after including the impact of RLD and RLR into a cost-based model and the impact of RID and RIR into a profit-based model, the load management programs result in similar cost savings, collectible revenue, profit, and customer benefits (from DLC program).
When remedies (RLD and RLR) are included in the cost-based model, the profits increase. However, when remedies (RID and RIR) are included in the profit-based mode, the profits decrease.
VI. LOAD MANAGEMENT PROGRAM IN A DEREGULATED ENERGY MARKET
Prior to deregulation, load management programs are used to minimize the cost of operation (cost-based) or the peak demand (load-based). However, as shown in section IV, cost-based model or load-based model does not guarantee maximum profit. A direct consequence from encouraging competitions in a deregulated energy market is the profit-oriented business operation. Thus, in a deregulated energy market, should profit-oriented load management programs (load-based and cash management economic models) be encouraged?
If the power industry was deregulated, and companies serving customer energy were allowed to make a profit, undoubtedly, customers should also be allowed to benefit from their own flexible and controllable demand. Even though companies making the highest profit may not necessarily provide the highest return to customers rendering controllable demand, they are among those that can provide customers the highest return from their controllable demand.
Given the objective of a load-based model that does not account for the cost of energy, the economic model will definitely not provide companies the best return from the programs. Also, a cost-based model does not guarantee companies the best return from load management programs because the model fails to consider the programs’ impact on revenue flow. Only profit-based objective that maximizes profit in the short-run and cash management model that maximizes profit in the long-run are capable of providing the highest return from the programs. Thus, companies adopting profit-oriented economic models are among those that can provide customers rendering their controllable demand the best deal.
Even
though cost-based model does not guarantee companies the highest return, the economic
model is still òvaluable
and should not be discarded totally. The
cost-based objective can still be used as a benchmark to evaluate the
effectiveness of the pricing mechanism and profit-oriented load management
programs.
Finally, will load management programs be favored in a deregulated energy market?
To our belief, the advent of deregulation
sheds some light on the prospect of adopting load management programs. At least, the three concerns that impede the
growth of the load management programs can be eliminated. Since companies serving customer energy are
driven to the energy market by the profitability of energy services, the
concern on the possibility of regulatory forced
programs is minimum. Any programs that
are not profitable (after including the impact of government incentives, if any)
will drive companies and customers alike away from participation. Also, since the customers are free to choose
any energy service providers, even to the extent of managing the demand by
themselves, any unfair programs will
drive customers away. If the load
management programs are used to tax non-participants,
customers not participating in the load management programs will choose to
leave the service any company that has treated them unfairly. Finally, as long as the load management
programs are profitable, why should one worry about the maturity of
technology? Even if the technologies
are not mature, as long as the technologies can provide companies the desired profit
margin at a given risk level, any competitive firms will be driven to adopt the
technologies. Thus, if there should be
any reason that the load management programs are forfeited, it should be the
unprofitable nature of the programs – nothing else!
VII. CONCLUSIONS
In this paper, various economic models for load management programs are presented and compared. The differences between a cost-based economic model and a profit-based economic model are also discussed. These economic models are presented to reflect their impacts on the load management programs to companies providing the services. In addition, by reviewing the load management programs prior to deregulation and by examining the programs’ impact in a deregulated energy market, this paper concludes that certain aspects impeding the growth of load management programs in the regulated environment are cleared. The profit-orientated business operation in a deregulated market can and will provide a more impartial evaluation on the potential market for the load management programs.
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IX. BIOGRAPHIES