IEEE Power & Energy Magazine - May/June 2016 - 76

in the other direction will be created even before the generator responds. Ignoring time dynamics, this has long been
understood by economists and is called the cobweb theorem;
depending upon the relative price response of the generator
and the load, the process can even be unstable. This is shown
graphically in Figure 3.
But if the ISO could reasonably anticipate the price
response of the load and adjust its balancing market accordingly, then it could avoid this phenomenon or mitigate it. The
time dynamics only aggravate the problem-the fast load
response is like a fast feedback loop, and if the price elasticity is high, then the feedback loop can be unstable. A further
complication is that many DR resources exhibit a "payback"
effect. Turning back a thermostat on an air-conditioning
system or a commercial refrigerator will reduce the demand
at that moment, but when the thermostat is restored to normal, the demand will increase above what it was to "repay"
the thermal mass of the building or refrigerator. A somewhat
similar effect known as cold load pickup is observed in distribution feeders with HVAC loads when, due to loss of load
diversity, abnormally high demands might be observed after
prolonged service interruptions (caused by coincident operation of HVAC units). Similarly, deferring the charging load
of an EV only increases the load at some future time when
(hopefully) it is cheaper or more easily served.
Storage introduces an even more dramatic result. In principle, storage used to time shift energy usage is exploiting
the price difference between two time periods, thus the time
arbitrage effect. If the price at 3 p.m. is higher than the price
at 2 p.m., it makes sense to store energy from 2 to 3 p.m.
and then discharge it from 3 to 4 p.m. If the storage device
is extremely efficient, then even a small price difference

justifies this arbitrage (meaning that losses incurred in
charging and discharging won't consume the small price
difference). But, if the relative price between the two hours
were to tumble, then the use of the storage reverses. In economic parlance, this means that the storage resource has
a near infinite elasticity that is both positive and negative.
That all but guarantees some interesting behavior arising
from the cobweb theorem if the market design does not recognize this effect.
We can learn two things from this discussion.
✔ The ISO and DSO markets have to understand the
price response of end-use load that is going to be responding to dynamic pricing (at real-time and hourly
levels) even when (and especially when) the load is responding autonomously without explicitly being in the
market as a bidder.
✔ The ISO and DSO market designs need to understand
the time dynamics of load and other DER response
and realize that price is not only a market mechanism
for clearing the markets but is also now a control signal and analyze things not only from the viewpoint of
market economics but also from the perspective of a
control system engineer.
These few simple examples illustrate the larger point: TE
holds great promise for integrating DERs into grid markets
and operations, and the potentially favorable market benefits
could very well incentivize customers to invest in and adopt
DERs faster than would otherwise be the case. But the ecosystem of TE is complicated, and the potential for unintended
consequences is definitely real. Therefore, serious analysis,
modeling, and simulation of proposed design, including representations of customer and DER behaviors economically

The Convergent Case: Each
New Outcome Is Successively
Closer to the Intersection of
Supply (S) and Demand (D).

The Divergent Case: each New
Outcome Is Successively
Further from the Intersection
of Supply (S) and Demand (D).
Price (P)

Price (P)

S

P3

S

P1
P3

P1

P2
D

P2
D

Q1 Q3

Q2

Quantity (Q)

Q3

Q1

Q2

Quantity (Q)

figure 3. Convergence and divergence in the cobweb theorem.
76

ieee power & energy magazine

may/june 2016



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