Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of indistinguishable drivers commuting between a common origin/destination pair in an acyclic transportation network. The drivers' route choices are affected.

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Morningstar Corporation>White Papers>Retrofitting Backup Power to a String Inverter System

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Overview –

The vast majority of grid tie PV systems are useless when grid failures
occur. They shut down at the very time that the electricity generated on site
is most needed. This does not need to be the case. There are a number of ways
to ensure that a PV array does not become stranded during utility outages, the
common thread between them all is that they utilize energy storage, additional
inverters and a variety of different power electronics depending on the system
design1.

System Types –

Each of the systems outlined below will achieve the goals of providing
secure AC power during utility outages. The systems all utilize existing
onsite PV for recharging batteries and powering daytime loads.

Battery Based Grid Tie Systems2 have a long and
proven history. Some of the very first residential grid tie systems in North
America were battery based and more than twenty years later many are still
going strong. However these systems are more complex, less efficient, and more
expensive. They are generally not a good choice unless the utility connected
customer wants the “off grid” experience.

Micro Grids3 are AC Coupled PV systems that are
designed to operate in stand-alone mode or utility interactive mode. These
systems integrate a battery-based inverter/charger that takes over controlling
the grid-tie inverters when utility failures occur. They are very efficient,
represent the current “state of the art” technology and are the most costly
choice for most emergency power applications.

AC Coupled Back Up Power Systems4 utilize a
battery-based inverter/charger to “fool” the GT inverter to “thinking” that is
still connected to the grid by supplying it with a AC signal5. Once the GT
inverter “qualifies” the AC signal (five minutes) it starts producing power
from the array, which is sent to the AC charger input of the battery based
inverter/charger. The power is used to power daytime loads and recharge the
batteries. AC Micro inverters are also used in AC coupling applications. The
principle is generally the same as with the larger string inverters although
they offer somewhat more design flexibility due to their more modular
nature.

Almost all retrofitted AC Coupled systems represent a series of
design compromises6. Systems must be designed so backup inverter and battery
bank can handle the entire output of the grid tie inverter plus a safety
margin. This results in system designs that are often unnecessarily large for
the intended purpose of providing a limited amount of back up power during
utility failures.

Another casualty of this design approach is the quality of battery
charge control during power outages. These systems often use a single stage
approach that turns the GT inverter off when battery voltage reaches a
predetermined level. Battery voltage is allowed to drop until a “reconnect”
threshold is reached at which time the GT inverter is turned back on. After a
five minute qualifying period the GT inverter begins supplying AC power for
use by local loads and the battery charger. This single-stage method of
charging may reduce the state of charge at the end of the day by as much as
20%. Sadly the AC Coupled system enters the second day of an extended power
outage with a battery of diminished capacity.

Interestingly a number of pre engineered AC Coupled system designs
utilize Morningstar controllers to improve the effectiveness of battery
charging management. In string inverter applications Morningstar TriStar
diversion controllers are utilized to “burn off” energy to keep the battery
voltage below the threshold that turns off the GT inverter. In micro inverter
systems the Morningstar Relay Driver is utilized to control groups of micro
inverters. When demand for current decreases the micro inverters are turned
off in groups. By doing so decreasing amounts of the available PV energy can
be supplied to the batteries to support their requirements. When demand
increases the Morningstar Relay Driver reconnects the AC signal to the micro
inverters that are turned off. After the five-minute qualifying period they
begin to contribute to the load and charging again.

DC Coupled Back Up Power Systems7
divert the output of the PV array away from the GT inverter to a MPPT Charge
Controller to convert the PV array string voltage to battery voltage (usually
48 Vdc). They operate independently of the GT inverter and as such the
connected battery based inverter/charger or UPS system can be sized to the
customers needs. This design approach often results in a simpler system that
can be installed at a lower initial cost.

DC coupled systems, by their very nature, put more power back into the
batteries during a power failure. The MPPT controller utilizes 4-Stage voltage
regulation to fully recharge the batteries during the solar day (providing
sufficient solar resource is available). This is a very important advantage if
the power outage extends beyond a few hours and into the evening hours because
batteries in a DC coupled system will end the first and subsequent days of a
power outage at a higher state of charge.

An additional advantage of this system is that it can accept an “oversized”
PV array without harm to the controller. During sunny conditions the
controller simply “ignores” input power that is in excess to its capabilities
or requirements.

During cloudy weather the controller can harvest energy from the entire
array and as such the likelihood of achieving a full charge is greatly
increased.

The inherent design flexibility of a DC coupled system allows the inclusion
of back up power into one leg of a three-phase PV array. The design paradigm
also allows DC installation on sub-arrays in large systems. DC coupling can
also be used as an effective way to increase the DC charging capacity of an AC
coupled system. With increased DC charging capacity the entire output of the
GT inverter can be passed through the back up inverter to support loads.
Additionally the effective capacity of the installed battery is “increased”
because the DC coupled part of the system completes a full charge cycle when
sufficient solar resource is available.

Summary –

Each of the types of system outlined above met the objective of
automatically providing a measureable and somewhat predictable amount of back
up power during utility power outages. They also had distinct advantages and
disadvantages. Full-time battery based GT systems and micro grids are most
suitable for applications where the grid will be used as a secondary source of
power and a place to ‘bank’ excess power. These systems, especially the micro
grids, are often designed so that the vast majority of the power is generated
and consumed on the customer’s side of the meter.

Both forms of dedicated GT PV back up power (AC and DC Coupled) have
advantages and disadvantages. In general the AC Coupled system is the best
choice for very small systems where the GT inverter is 3 kW of less. AC
coupled systems also are an excellent choice where there are very high demands
for power delivery on the first day of a power outage or where the combined
capacity of the battery inverter and the GT inverter will be called upon
during the solar day. DC Coupled systems are superior in most other
residential and light commercial applications largely due to their simplicity
and flexibility with respect to inverter and battery bank choice.

The table below highlights some of the advantages and disadvantages of both
types of systems

AC Coupled

Advantages

  • The backup inverter(s) and batteries must be sized to accommodate the
    full output of the existing grid-tied inverter.
  • Can combine the output of the solar array and the back up inverter to
    support loads during a power outage (day time only).
  • Well-understood application with kitted solutions.

Disadvantages

  • Crude on/off overcharge protection does not fully recharge the
    batteries during power outages, which can result in diminished capacity
    during long duration outages.
  • Often requires additional control relays.

Morningstar DC Coupled

Download Gtsystems Driver

Advantages

  • Back up system inverter and battery bank sizing completely independent
    from the grid tie inverter. Can be sized to suit customers’ needs and
    budget.
  • Uses 4-Stage charge voltage regulation to attain 100% SOC when
    sufficient solar resource is available.
  • Can handle oversized PV inputs with no harm to controller, which allows
    for greater energy harvest on cloudy days.
  • Offers a simple way to provide single phase back up power on three
    phase systems.
  • Lowest total cost for entry-level systems.
  • Can be installed in sub-array wiring for large arrays.
  • Additional units can be installed in parallel for increased battery
    charging/load support capacity.

Download Gt Systems Drivers

Disadvantages

  • Greater number of components to install in some installations
    only.
  • Manual switch operation.

Conclusion –

DC coupling makes the most sense for most GT applications that require
battery back up capabilities. The advantages far outweigh the disadvantages
and the Morningstar DC Coupled system offers the lowest cost and best
performance for comparably sized GT systems.

1 SMA offers a “secure power” feature that puts out up to 15 amps AC during
utility interruptions however the output varies with the available solar
resource. Because the output of these inverters is not stable and they don’t
provide power at night they are not addressed in this article.

Download gt systems driver download

2 Examples include the Schneider XW series, and Outback GTFX modes.

3 Examples include the SMA Sunny Island series.

4 Examples include Outback Radian and some Magnum inverters

5 The reason that PV arrays become stranded during utility outages is that
the Grid Tie inverter cannot operate and process power without an AC reference
voltage from the utility. They are designed this way to prevent them from
“islanding” which is a term which refers to sending power onto a shutdown
utility grid. It is an important safety protection for utility workers.

6 The exception is retrofitting a Sunny Island to an existing SMA grid tie
system. This solution is very effective as the inverters are designed to
communicate with each other. It is also, in most cases, the most costly
option.

7 Examples include the Morningstar integrated Transfer Switch/600Vdc MPPT
Charge Controller.

Download PDF
Abstract: Stability of Wardrop equilibria is analyzed for dynamical transportationnetworks in which the drivers' route choices are influenced by information atmultiple temporal and spatial scales. The considered model involves a continuumof indistinguishable drivers commuting between a common origin/destination pairin an acyclic transportation network. The drivers' route choices are affectedby their, relatively infrequent, perturbed best responses to global informationabout the current network congestion levels, as well as their instantaneouslocal observation of the immediate surroundings as they transit through thenetwork. A novel model is proposed for the drivers' route choice behavior,exhibiting local consistency with their preference toward globally lesscongested paths as well as myopic decisions in favor of locally less congestedpaths. The simultaneous evolution of the traffic congestion on the network andof the aggregate path preference is modeled by a system of coupled ordinarydifferential equations. The main result shows that, if the frequency of updatesof path preferences is sufficiently small as compared to the frequency of thetraffic flow dynamics, then the state of the transportation network ultimatelyapproaches a neighborhood of the Wardrop equilibrium. The presented results maybe read as a further evidence in support of Wardrop's postulate of equilibrium,showing robustness of it with respect to non-persistent perturbations. Theproposed analysis combines techniques from singular perturbation theory,evolutionary game theory, and cooperative dynamical systems.

Submission history

From: Giacomo Como [view email]
[v1]Tue, 11 Jan 2011 21:45:25 UTC (63 KB)
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