# Tariff Market

## Contents

# Tariff Market

Brokers acquire customers by offering tariff contracts. Customers are always under contract with some tariff. They will evaluate the available tariffs with respect to their own preferences, and may *subscribe* to one of the offered tariffs subject to the relative attractiveness compared with their current tariffs, and subject to an *inertia* factor that represents their general lack of attention to incoming junk mail.

## Tariff representation

A Tariff is a structure composed of Rates, with applicability rules, as shown here.

- Tiered rates, in which customers pay/receive one rate for a portion of usage (up to 20 kWh/day, for example), and a different rate (or set of rates) for the remainder. For example, a fixed rate could apply for the first 20 kWh/day, and another fixed rate could apply above that level on weekends, while a variable rate could apply on weekdays for the excess usage.

- Time-of-use rates would have a set of fixed rates for different intervals. The simplest form would be a night rate from perhaps 20:00 through 7:00, and a daytime rate from 7:00 through 20:00.

- Separate weekday and weekend rates.
- Two-part tariffs (fixed daily fee plus usage fee). The fixed fee is represented as the "periodicPayment" in the Tariff.

- Signup payments in either direction (fee or bonus), represented as positive or negative signupPayment values.

- Early withdrawal penalties.
- Variable rates with minimum and maximum values, estimated mean values, and notice intervals. The noticeInterval field in the variable rate is the minimum delay between a broker announcing a price change and the price change taking effect. So a noticeInterval of 2 hours would give customers at least a 2-hour notice of a price change. More specifically, for a rate with a 2-hour notice interval, the price change would take effect at the beginning of the third timeslot following the price-change announcement.

This structure does not allow a feature found in some real-world tariff examples: "Sign-up for a 6-month contract and you get the first month free," or "get 30% off for the first two months" or some other time limited rate specification."

A tariff applies to only one "Power Type" for a Customer. Power Type is a type of power consumption or production that is separately metered. A Customer with multiple Power Types will need to subscribe to multiple Tariffs. Primary power types are

**Consumption:**ordinary power consumption, not remotely interruptible. Customers may, of course, adapt to price variations (time-of-use or variable rates, for example) by shifting their usage with respect to their "baseline" consumption profiles.

**Interruptible consumption:**power consumption that can be remotely interrupted. Typically this type of usage is connected to energy storage devices, such as water heaters or heat pumps, or even batteries. Brokers presumably induce Customers to allow interruption of their air conditioning systems by offering lower rates than they pay for ordinary consumption.

**Energy production:**devices that produce power under certain conditions. Specific types of production supported in the simulation include:**Solar panels:**have a nominal capacity, which is the output at noon under a clear sky. The simulation models day-length and cloud cover, but not changing insolation angle.**Wind turbines:**have a nominal capacity, the output when the wind is blowing at 40 km/hr.**Combined heat and power:**or CHP systems are gas turbines that produce both power and heat. They produce power when the customer needs heat, and so their output is sensitive to the current temperature.

**Electric vehicle:**charging/discharging of electric vehicles.

## Tariff and Subscription lifecycles

Tariffs may be offered by Brokers at any time, and Customers may subscribe to offered Tariffs at any time. When a Tariff is first offered, it has no subscribers. Until it has at least one subscription, the Broker may withdraw it at any time.Once a Customer subscribes to a Tariff, it becomes active, and continues to be offered for new subscribers. Tariffs may have an expiration date; once that date passes, existing subscriptions continue, but new subscriptions are not allowed. Once the last subscription is removed, the Tariff is no longer in the market.

A broker can withdraw a Tariff that has no subscriptions. Once a tariff has subscriptions, withdrawing a tariff has the effect of not allowing new subscriptions. A tariff with subscriptions may be forcefully withdrawn or *killed*, in which case existing subscriptions are transferred to the succeeding Tariff. Presumably the Broker will have offered a new Tariff that 'supersedes' the withdrawn tariff first. If not, then subscriptions will revert to the initial default tariff.

*T1*, it pays the subscription fee (which is probably negative, making it a sign-up bonus), and begins operating under the terms of

*T1*. If the Broker decides to supersede

*T1*with a new Tariff

*T2*, then the Customer's subscription is changed to Tariff

*T2*, except that the early-withdrawal penalty of

*T2*is waived for this subscription. In other words, if a Broker switches a Customer's subscription, the Customer can switch Brokers without penalty. If a Customer decides to switch its subscription from Tariff

*T1*to another Tariff

*T3*, then its subscription is switched, after paying any early-withdrawal penalty due under the terms of

*T1*as well as the subscription cost of

*T3*.

## Customer population models

Population models represent potentially large groups of households or businesses that are similar to each other in interesting ways. Since these models represent populations, they are typically involved in multiple subscriptions. Customers have busy lives, and usually they discard the junk mail that arrives each day advertising new tariffs. However, with some low probability, a few customers will compare the available tariffs with the one they have, and may decide to switch. This creates a new subscription for some (usually quite small) portion of the population represented by the model. That sub-population, of course, already had a subscription to some other tariff, and so the population counts on those other subscriptions are reduced when customers switch tariffs. The only rule is that the entire population has a subscription to some tariff at all times.

If customers switch to a new tariff that does not have an early-withdrawal penalty, then they can simply join an existing subscription to that tariff. However, if they are switching to a tariff that DOES have an early-withdrawal penalty, then they can only start a new subscription, or join an existing subscription with the same expiration date.

## Individual customer models

Large energy users, such as industrial facilities, shopping malls, colleges, or municipalities, will be represented by individual models. These Customers may engage in negotiation with Brokers, by submitting a counteroffer, in the form of a Tariff structure, in response to any current Tariff. Such a counteroffer is sent to the Broker who published the original Tariff. Of course, there is nothing to stop such a Customer from submitting the same Tariff proposal to all Brokers.

In order to evaluate such a counteroffer, the Broker needs to know the demand and supply profiles of the Customer, along with capacity and constraint information about any remotely interruptible energy sources or loads that would be covered by the proposal.

## Tariff evaluation

When tariffs are published, tariff customers may choose to subscribe to tariffs by comparing the utilities of the tariffs on offer, including the current tariff if it remains available, and choosing one that approximately maximizes utility.

The probability that a given customer will bother to make a choice at all is governed by an Inertia parameter *I* between 0 and 1, giving the probability that the customer will *not* evaluate tariffs during a particular tariff-publication event. To model the market opening at the beginning of the game, we expect customers to be paying attention, and so the actual Inertia parameter *I _{a}* is

(1)I=_{a}I* (1 - 2^{-n})

at the *n*th tariff publication event. In other words, all customers evaluate tariff offerings in the first publication cycle, but their interest tails off quickly. For a population model, (1 - *I _{a}*) is the portion of the population that will evaluate tariffs and possibly switch.

For a tariff *i* (where tariff_{0} is the current tariff), utility *u _{i}* is expressed as the weighted sum of an energy cost factor and a risk factor. The energy cost factor is the ratio of the cost of energy under the default tariff to the cost under tariff

*i*, so a lower rate/kWh results in higher utility. The energy cost factor

*f*is computed as

_{ce}(2)f= sum_{ce}_{t}(C* -_{e,t}p) / (sum_{def}_{t}(C* -_{e,t}p-_{v,i,t}p) -_{p,i}p-_{signup,i}F*_{f}p-_{withdraw,i}p_{withdraw,0})

over some expected subscription duration [*t*=0 .. *t*=*d _{e}*] for expected consumption

*C*. Fixed costs/payments include periodic payments

_{e}*p*, and signup

_{p,i}*p*and withdrawal

_{signup,i}*p*payments. When evaluating the current tariff, the signup payment for the current subscription is zero, the withdrawal payment is zero because it does not have to be paid if the customer opts not to switch. Withdrawal payments for alternate tariffs are discounted by a factor

_{withdraw,i}*F*=

_{f}*d*

_{i}/

*d*, which preferentially discounts shorter commitment intervals

_{e}*d*. The fixed cost/kWh of the default tariff is given by

_{i}*p*. Note that for a tariff with no expiration date, the withdrawal payment does not apply, and so the values of

_{def}*F*and

_{f}*p*are not needed and can be set to 0.

_{withdraw,i}The utility of tariff *i* is then

(3)u=_{i}f-_{ce}r*_{i}w_{r}

where *r _{i}* is the customer's "risk" assessment for the tariff, and

*w*is a weighting factor that represents the customer's risk tolerance (higher values of

_{r}*w*represent higher levels of risk-aversion).

_{r}When a tariff contains one or more variable rates (dynamic pricing), customers compute a risk-adjusted estimate of the actual cost. Four values must be combined to generate an estimate for a variable-rate tariff:

(4)p=_{v}alpha* (p*_{em}w+_{em}p*_{max}w) + (1 -_{max}alpha) *p_{r}

where *p _{em}* is the broker's claim of expected mean price,

*p*is the brokers commitment to the maximum value for the rate, and

_{max}*p*is the realized price for

_{r}*KWh*, the total power sold through the tariff so far. The weights are constrained such that (

_{total}*w*+

_{em}*w*) = 1. The parameter

_{max}*alpha*is used to adjust the weight given to the realized price based on

*KWh*, as

_{total}(5)alpha= 1 -w* (1 - 1 / (1 +_{r}KWh/_{total}KWh))_{0}

where *w _{r}* = [0..1] and

*KWh*are parameters specific to each customer. The assumption is that the actual realized price is more predictive for a tariff with a more substantial price history (larger amount of power sold).

_{0}The set of tariffs considered is a subset of tariffs that are applicable to the given PowerType, and that are more attractive than the default tariff for that PowerType. Because tariff evaluation has some cost, and because we wish to discourage the practice of "flooding" by brokers who want their tariffs to have a better chance of being chosen, customers evaluate only the most recently published *N* tariffs from each broker, where *N* is at most 5 of each type. So for an electric vehicle, there could be EV tariffs, interruptible-consumption tariffs, general storage tariffs, and simple consumption tariffs that all apply. If a broker has published 5 of each type, then for that broker, *N* = 20.

If a customer is subscribed to a tariff that is superseded and canceled, then by definition *d _{i}* = 0 for the new (superseding) tariff and therefore there is no withdrawal penalty. In addition, the

*I*value for the affected customers is reduced to

(6)I=_{s}I/df

for all subscribers to the superseded tariff at the next tariff evaluation interval. The parameter *df* is a "distrust factor" that will probably be set to 2 for now, but could be affected by broker reputation in the future.

Finally, customers are not entirely rational, and so they do not always choose the most attractive tariff, but they are more or less biased toward more attractive tariffs. Tariff choice will be based on the logit choice model as outlined in the 2012 Power TAC specification.

## Initial state of the market

At the beginning of the scenario, all customers are subscribed to a relatively unattractive fixed-rate tariff with a default Broker. This tariff is always available, and so if a Broker kills a tariff without replacing it, the customers subscribed to it will revert to the default tariff. This also serves to put a cap on market prices.

This condition is typical of the beginning of a market liberalization process, in which an existing regulated utility (the incumbent) owns all the customer accounts, and incoming Load Serving Entities (Brokers) must attract the customers away from the incumbent.