FAST SIMULATION ALGORITHM FOR PV SELF

Presented at the 29th European PV Solar Energy Conference, Amsterdam, September 2014
FAST SIMULATION ALGORITHM FOR PV SELF-CONSUMPTION WITH HEAT PUMP SYSTEMS:
CALIBRATION METHODOLOGY WITH COMPREHENSIVE DYNAMIC SIMULATION MODEL AS
REFERENCE
Andreas Witzig1, Thomas Straub2, Matthias Hartmann2, Torsten Sonntag2
1
Vela Solaris AG, Winterthur, Switzerland
2
SMA Solar Technology AG, Niestetal, Germany
Corresponding authors: Andreas Witzig, +41 55 220 71 01, [email protected]
Thomas Straub, +49 561 9522 3125, [email protected]
ABSTRACT: Self-sufficiency of systems with photovoltaic (PV) energy production gets more and more important.
Demand side management with the use of heat pump and thermal energy storage has proven to be an efficient and
effective means for increasing the PV self-consumption ratio [1, 2]. Accurate prediction of the self-consumption and
the resulting self-sufficiency quota requires a comprehensive simulation including heat pump characteristics, thermal
balance of the building and hot water demand profiles. These simulations are usually elaborate and time consuming.
This work presents a fast but reliable estimate of the system’s PV self-consumption potential. It is based on the wellknown tool Sunny Design [3], which has been extended by the capability to calculate the building and hot water
energy demand, and applying heat pump model with realistic characteristic curves. The proposed algorithm is capable
of including battery storage and advanced controllers as future extensions. The algorithm is in accordance with the
physics-based simulation tool Polysun which includes device physics as well as controller details with a tight
coupling between the electrical and the thermal part of the system [4]. The newly introduced model parameters in
Sunny Design are calibrated and validated with the detailed Polysun model.
Keywords: PV self-consumption, load management, heat pump, simulation, Sunny Design, Polysun.
1.
prerequisite of any photovoltaic simulation and in
general, it can be recognized that the time resolution has
to be at least one hour but accuracy still increases with a
smaller time step. Sunny Design applies a five minute
time step and Polysun has a variable time step down to a
few seconds.
The strength of Polysun is that in addition to the
electrical calculation, it analyses the hydraulic topology
on the thermal system and calculates the fluid flow in all
pipes [5], its application for modern energy efficient
buildings [6] and combined photovoltaic and thermal
systems [7]. The simulation model therefore also includes
pumps, three-way valves, heat exchangers and thermal
storage tanks with stratification (as displayed in Figure 1)
as well as the detailed control algorithms in the system.
Sunny Design, the dimensioning and PV yield
prediction tool of SMA Solar Technology AG, has been
extended with a building and hot water heat demand
model and a heat pump model in the course of this work.
A fast CPU execution time is crucial for this application.
In the course of the presented joint work, a MATLAB
script has been developed which is translated into Sunny
Design. The intermediate simulation results presented in
this work with the “fast algorithm” are typically shown
out of MATLAB and are not available in the graphical
user interface of Sunny Design.
INTRODUCTION
1.1. Motivation
PV self-consumption optimization recently received a
lot of attention. In many cases demand side management
is more effective and cheaper than the usage of battery
systems or is used in combination with electrical storage.
In particular, the combination of heat pump heating
systems with PV rooftop installations is promising and
potentially offering a relatively high self-sufficiency
quota. It is important to recognize that the coupling
between electrical and thermal systems has the advantage
to utilizing already existing thermal storage elements (hot
water storage tank or thermal inertia of buildings), which
typically have a time constant of about one day and
experiencing no deterioration also with high number of
charging and discharging cycles.
Simulation of PV self-consumption with heat pump
systems as a part of the planning process today exceeds
the services a typical PV system specialist offers and has
up to now mainly been done in research institutes and in
the academic world. This work contributes by
simplifying the planning process and providing ready-touse simulation tools for several stages in the planning
process. Namely, the planning software Sunny Design
and the comprehensive simulation tool Polysun offer new
functionality that facilitates PV self-consumption
calculation and optimization. A good agreement between
the tools increases planning certainty and result
reliability.
1.3. Scientific results
This work describes a general procedure to bring
simulation models of different detail-levels in agreement
and is effective for many other algorithms beyond the
specific above mentioned commercial applications. A
calibration methodology is presented that allows
implementing a very fast yet accurate and easy to use
algorithm, based on a more detailed comprehensive
1.2. Starting point
Both simulation models are based on a time-stepping
algorithm and comprise the yield calculation of
photovoltaic modules and inverters. This is an important
1
Presented at the 29th European PV Solar Energy Conference, Amsterdam, September 2014
simulation model.
The advantage of using models on several detail-levels
is that model parameters in the fast model can be
determined by calibration against the comprehensive
model. The fast model can be reduced to a very small set
of parameters, which makes it very lean and easy to use.
An important part of the work lies in the definition of a
large number of system details in the comprehensive
model. These details are all comprised in the small
parameter set of the fast model resulting by the
calibration procedure. Publishing the comprehensive
model makes the procedure transparent and implicitly
lists all the model assumptions based on physical
rationale. In de-centralized energy systems, controller
settings are key influencing variables and it is important
to model them in sufficient accuracy also in the fast
model. In consequence, innovative components or
controller strategies can easily be accounted for.
A concise set of default values is proposed, built into
the software tools and discussed in this paper. User can
make a quick simulation easily and if required can go
into more detail if necessary.
systems with heat pump in comparison to the system
without heat pump.
2.
SIMULATION ALGORITHMS
2.1. PV Self-consumption calculation
For the owner of a PV power plant the most important
figure is the total energy production per year. Secondly,
he will relate the energy production to the energy
consumption and he may typically recognize that in
summer he is a net energy producer while in winter he is
a net energy consumer.
Figure 3: Example results for the electricity production
and consumption in a typical plus-energy house with a
roof-top PV installation.
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In the view of the house owner, it may seem natural to
look at the summation of the energy balance over year or
over a month. However, since the power grid is more and
more in a focus with a large portion of photovoltaic
energy production in summer, it is important to consider
the power to and from the power grid at any instant in
time. As a general rule, the self-consumption ratio is the
highest number if yearly sums are divided (as in the
definition of a “plus-energy house”). It becomes smaller
if the energy balance is calculated on a monthly basis and
even smaller if hourly values are considered. In reality,
instant power values are relevant, and in many
applications, the resulting self-consumption is
considerably smaller than expected.
In consequence, detailed electrical consumption profiles
are a key input parameter for any simulation in the
planning phase of a PV system. Within this study we
used a measured domestic electricity consumption profile
published in reference [8]. This profile for medium
energy consumption has a time resolution of 5 minutes.
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(5)
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(6)
(4)
Figure 1: Polysun simulation used in this work. The
system is also available as a company template in the
release version of the Polysun software. Components: (1)
PV field, (2) inverter, (3) electrical consumption profile,
(4) heat pump, (5) floor heating with building model, (6)
storage tank, (7) hot water tap.
Energy yield
8,707 kWh
Self-consumption
2,914 kWh
2.2. Building model
For the evaluation of the heat pump power consumption
profile, it is required to calculate the building heat
demand. The building is modeled with a single node
dynamic model where the thermal losses through
windows and walls play the major role, followed by
ventilation and infiltration losses. Solar thermal gain
through the windows and thermal gain from people and
equipment inside the building are also accounted for.
Note that passive solar gains are considerable,
especially for modern well-insulated buildings. They
have to be included in order to model the thermal balance
of the building accurately. The models for solar thermal
gains differ significantly between the fast and the
comprehensive algorithm. In the fast algorithm, the
passive solar heat gain 𝐺psh of the building is
proportional to the global irradiation 𝐺(𝑡) from the
weather data.
Grid feed-in
5,793 kWh
Consumption
9,121 kWh
Figure 2: Sunny Design simulation results. Selfsufficiency and self-consumption quotas are calculated
and displayed together with a graphical representation of
the yearly energy balance. The tool always shows the
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Presented at the 29th European PV Solar Energy Conference, Amsterdam, September 2014
𝐺psh(𝑡) = 𝐴(𝑡) ∙ 𝑢 ∙ 𝑊𝑊𝑅 ∙ 𝑆𝐻𝐺𝐶 ∙ 𝑆irr ∙ 𝐺(𝑡)
with the window transmittance 𝑢, the window-to-wallratio 𝑊𝑊𝑅, the solar heat gain coefficient 𝑆𝐻𝐺𝐶 and 𝑆irr
being a scaling factor used for calibration (see Section
3.2).
In the comprehensive simulation, the solar gain is
calculated by evaluating the solar irradiation on every
wall of the building according to the angle of incidence.
At a lower position of the sun in winter, there is
automatically more solar irradiation in the comprehensive
model. In the simplified model, the excess passive solar
gain in winter is accounted for by the formula
Figure 6: Building heat demand, monthly average,
comparison between Polysun and Sunny Design. The
differences during the months are due to the difference of
the passive solar gain. The irradiation through the
windows is calculated geometrically in Polysun and is
approximated with a lumped model in the fast algorithm.
𝐴(𝑡) = 1/(1 − 𝑎 ∙ cos(2π (t + 10 days))
with the angle modifier factor a as a fit parameter and a
phase shift of 10 days between the winter solstice on
December 21st and the start of the simulation period on
January 1st. The resulting agreement between the solar
gain calculated by the fast and the comprehensive
algorithm is shown in Figure 4.
As it can be seen in the Figures 5 and 6, the passive
solar gain provides sufficient energy to the building for
more than four months of the year. In the specific
example, no heat demand occurs for mean outside
temperatures above 10°C.
The fast algorithm assumes that the building heat
demand is always met but that the heating system only
switches on as soon as a certain energy deficit is
accumulated. The level of energy deficit that is allowed is
a measure for the thermal inertia of the building.
In a similar manner as for room heating, the heat
demand of the hot water production is calculated: the
accumulated energy deficit is treated separately due to its
different temperature level. It is assumed that the hot
water demand has always a priority over the building heat
demand.
The comprehensive model applies a plug-flow
technique and accounts for the specific hydraulic
topology of the system of choice. It includes pipe details
and accounts for thermal losses through the pipes.
Furthermore, it assumes that thermal storage tanks are
used and – next to the thermal losses of the storage tank –
simulates natural stratification and mixing of fluids with
different temperature levels.
Figure 4: Passive solar gain is the main energy input for
a well-insulated modern building. In winter, it covers
most of the building heat demand and in summer,
additional ventilation losses are required (people open the
windows) in order to prevent overheating.
2.3. Heat pump model
In the system under consideration, an air-water heat
pump is applied as the only heating system installed to
cover the building heat demand (monovalent system).
The heat power delivered to the building from the heat
pump is therefore required to cover the heat demand of
the building also during the coldest time of the year. It is
assumed that a low temperature heating system
(underfloor heating) is applied. An inflow temperature of
35°C is assumed for the heating system.
Furthermore, it is assumed that the same heat pump is
used to provide the heat for the hot water. A heating
temperature of 55°C is assumed.
The heat pump efficiency strongly depends on the
temperature difference between the primary side of the
heat pump (outside temperature) and the secondary side
(temperature level of the floor heating or the hot water,
respectively). Note that the assumed temperature levels
for the required heat are relatively low, which is in favor
of the heat pump system and are the state-of-the-art in
modern energy-efficient buildings.
In the fast algorithm, built-in characteristic curves for a
typical heat pump are applied according to Table I and II.
The different efficiencies for the higher temperature (hot
water production) and the lower temperature level
(heating of the building) are reflected in these curves.
Figure 5: Building heat demand, daily average,
comparison between Polysun and Sunny Design. It can
be seen that the Polysun calculation shows higher peaks
due to a more detailed building model.
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Presented at the 29th European PV Solar Energy Conference, Amsterdam, September 2014
Table I: Characteristic curve for heat pump when used
for heating (assuming floor heating at 35°C)
Tamb °C
Pheat kW
Pel kW
-20.0 -15.0
4.5
2.1
4.9
2.1
-7.0
6.4
2.2
2.0
7.0 10.0 20.0
8.5 10.7 11.8 12.0
2.3 2.4 2.4 2.4
Table II: Characteristic curve for heat pump when used
for hot water production (hot water temperature at 55°C)
Tamb °C
Pheat kW
Pel kW
-20.0 -15.0
3.2
3.1
4.4
3.1
-7.0
2.0
7.0 10.0 20.0
6.2
3.1
7.5
3.3
9.7 10.5 11.0
3.4 3.5 3.6
Figure 7: Hot water profile, summation over each day of
the year. The detailed profiles also show a realistic intraday time variation, which is not visible in this figure.
2.6. Weather data
For the calculations in Sunny Design, the characteristic
curves are taken from a 20kW heat pump. Pel and Pheat are
the electrical power into the heat pump and the heat
power at the output of the heat pump, respectively. For
heat pump sizes other than the 20kW nominal power, Pel
and Pheat are scaled accordingly.
In Polysun, heat pumps are characterized with more
supporting points, typically originating from the
standards EN 255 and EN 14511. If available, more
measurement points can be entered in Polysun. In all the
available points from the heat pump characteristics,
Polysun interpolates with the scattered data interpolation
algorithm [9].
Choosing the correct size of the heat pump is in reality
crucial because a too big heat pump reduces the
efficiency of the system. However, a too small heat pump
that is not capable of covering the requirements in the
coldest time of the year is a severe malfunction resulting
in complaints and expensive service work. In the
simulation, the thermal power from the heat pump is
adjusted such that the heat pump runs continuously
during the coldest 48 hours of the year. Furthermore, an
oversizing factor is introduced which takes into account
that the weather data represents a typical year and the
heat pump system is also required to cover the building
heat demand for an extremely cold winter.
In consequence, the heat pump size is automatically
chosen such that the heat pump is driven in pulse
operation, switching on and off several times per day.
As a prerequisite, weather data for specific locations are
required, including ambient temperature and solar
irradiation. Both the fast and the comprehensive
algorithm use marching-on-in-time algorithms which
span over an entire year in order to reflect the different
seasons as well as the natural fluctuations of the weather.
Therefore, weather data based on monthly or daily basis
is not sufficient as an input, but has to be provided at
least in arrays of every hour per year. In any calibration
activity or when comparing different simulation tools
with one another, it is absolutely necessary to have
exactly the same weather data as an input. For the
calculations presented in this work, a weather data set for
Kassel, Germany, was used which had been generated
using the software Meteonorm [10].
2.7. The art of choosing good default parameters
It is important to request the right information from the
user of the simplified software and to choose adequate
default parameters for the information that is not
available in the typical situation when the software is
applied. In the case of Sunny Design, it is feasible (and
necessary) to ask about the buildings size and insulation
standard. However, it is not an option that the user has to
care about the window areas and glass type since this is
in general unknown to the PV planner. In Polysun on the
other hand, more details about the building can be
entered, as for example the window-to-wall-ratio for the
different directions south, east, north and west and the
solar energy transmittance coefficient for the window
glasses.
Default values are chosen according to well-known
standards, if they are available. As an example, heat
transmission coefficients according to Table III have
been chosen for the five different building types that are
offered in Sunny Design.
2.4. Heating controller
The heating system controller that drives this operation
is modeled in the comprehensive simulation with Polysun
as well as in the fast simulation with Sunny Design
because for future use of this algorithm, switching on and
off the heat pump needs to be modeled in much detail,
carrying a high optimization potential.
Table III: Different building types offered in Sunny
Design.
2.5. Hot water profile
Building type
The hot water energy demand shows two daily peaks,
one in the morning and one in the evening. At weekends,
it is assumed that 14% more water is used, and a lower
water consumption in summer is assumed, as it is shown
in Figure 7.
overall heat transmission coefficient
Passive house
New building, well insulated
Average residential building (2010)
Average residential building (2000)
Building not modernized (<1995)
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0.17 W/K/m2
0.24 W/K/m2
0.34 W/K/m2
0.50 W/K/m2
0.80 W/K/m2
Presented at the 29th European PV Solar Energy Conference, Amsterdam, September 2014
Secondly, the two variables “irradiance scaling” 𝑆ir and
“building shell scaling” 𝑆bs are used to obtain the
agreement in the heat demand from the building. While
𝑆ir appears in the formulas as a pre-factor to the global
irradiance from the weather data, the second parameter
𝑆bs scales the building shell heat loss and appears in the
product with the building shell area and the heat
transmittance. A model agreement has to be found for
different building types and different locations, i.e. for
various building heat demands. In an exemplary manner,
Figure 8 shows how a variation of the desired indoor
room temperature and the effect of different fit
parameters influence the agreement between the
comprehensive and the fast algorithms.
In a next step, it has to be ensured that the dynamic
behaviors of the fast and the comprehensive algorithms
are in agreement. The time constant of the building
𝜏building represents the thermal inertia. Furthermore, the
fast algorithm has two controller parameters which are
the trigger points to switch on the heat pump for heating
heating
hotwater
or for hot water production, 𝜗trigger and
𝜗trigger
,
respectively.
Table IV: Main default parameters
Parameter
Default value
Building floor height
Internal heat gain in the building
Air change (causing ventilation heat loss)
Desired room temperature
Hot water temperature
Nominal inlet temperature floor heating
Cold water temperature
Solar heat gain coefficient
Solar energy transmittance through windows
2.5 m
1.5 W/m2
0.3 1/h
21 °C
50 °C
35 °C
10 °C
0.85
0.5
Simulation projects done with the comprehensive model
Polysun are provided in order to make the choice of
default
parameters
transparent.
Having
the
comprehensive model at hand, it is not only possible to
obtain these values but also to recognize the influence
they have on the simulation.
3.
MODEL CALIBRATION AND VALIDATION
3.1. Consistency of parameters and input data
In the comparison between the fast and the
comprehensive simulation algorithms, first it has to be
ensured that the same input data is used for the weather
data, the hot water and electrical consumption profiles,
the characteristic curve of the heat pump.
A selection of building model parameters from Polysun
is offered in Sunny Design, which is summarized in
Table IV.
In the fast algorithm, several parameters, such as the
energy storage capacity of the building and the thresholds
for switching on the heat pump due to an accumulated
building heat demand have to be determined. In the
calibration procedure, the above parameters are chosen
such that the heat pump runtime, the number of switching
on, and the total thermal energy from the heat pump
match between the fast simulation and the comprehensive
simulation. The goal is that monthly values match well in
order to make sure that seasonal effects are well covered.
Figure 8: Calibration of the fast algorithm. The building
heat demand depends on the desired indoor room
temperature. The pairs 𝑆ir and 𝑆bs have to be chosen such
that an optimal fit is found in comparison to the Polysun
reference. “Fit-2” shows good agreement with the scalar
parameters 𝑆ir=2.8 and 𝑆bs =2.1.
3.3. Results comparison
The simplifications in the fast simulation algorithm
introduce some model inaccuracy. However, compared to
the uncertainties in the input data (hot water
consumption, weather data), the agreement between the
fast algorithm and the comprehensive model is still good
(see Table V and Figure 9). Furthermore, examining the
time domain simulation results it is clear that the heat
pump is in pulsed operation most of the time, even in
winter (Figure 10). In order to obtain a good selfconsumption ratio, the PV field has to be large enough in
order to cover the power consumption requirement from
the heat pump. The potential to increase the selfconsumption ratio by a smart controller depends on the
thermal storage capacity of the heating system.
3.2. Calibration parameters
The agreement between two different simulation
models can be recognized as a non-linear optimization
problem. While the comprehensive model is based on
physical formulae and detailed information about the
system (such as pipe diameter and length, storage tank
dimensions and insulation properties), the fast model has
some built-in fit parameters. The calibration of these
parameters is an important procedure in the model
development and it is important for the acceptance of the
new fast algorithm that the calibration procedure can be
reproduced.
In a strictly methodical approach, a scalar measure is
defined to evaluate the agreement between the two
numerical models. However, different from a rigorous
numerical optimization problem, engineering know-how
about the system behavior is also used in the fitting
procedure, bringing not only some final results in
agreement but also some intermediate variables: A first
variable “hot water scaling” 𝑆hw is used to force an
agreement in the hot water energy demand.
Table V: Result comparison between Polysun and Sunny
Design for the building type “New building, well
insulated”, 220 m2 heated floor area and an annual hot
water demand of 146 m3 (8 people).
Variable
Unit
Polysun Sunny Design
Heating demand
Hot water demand
5
kWh/a
kWh/a
11126.6
6998.2
11208.0
7133.4
Presented at the 29th European PV Solar Energy Conference, Amsterdam, September 2014
New trends include the use of modulating heat pumps
for a better match to the PV power production [9] and the
application of smart control strategies [11]. The presented
algorithm is capable of covering such systems. While the
comprehensive simulation model covers these topics, the
current version of Sunny Design is optimized for simple
user interaction and does not yet comprise this level of
complexity.
In many regions of the world heat pumps are more often
used for cooling than for heating, providing a huge
potential for PV self-consumption operation. The
presented algorithms are well capable to cover this
application range and a very high potential for efficiency
optimization is recognized in this field.
Figure 9: Result comparison between Polysun and Sunny
Design show good agreement for the heat pump
operation time.
5.
The authors want to thank E. Vrettos and Dr. S. Koch,
(ETH Zurich) and Prof. Dr. Zogg, (University of Applied
Sciences and Arts Northwestern Switzerland) for fruitful
discussion and advice. The work has partially been
financed by Swiss Electric Research.
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6.
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Figure 10: Electrical input power of the heat pump (blue
line, left axis), solar gain (green line, left axis), and
ambient air temperature at the air-water heat pump (red
line, right axis). Note that the heat pump runs in different
states depending on if it is producing heat for hot water
(1) or heating for the building (2). The plot shows the
operation in the end of January and it can be seen that the
heat pump operates continuously at night for several
hours but is in pulsed operation most of the time.
CPU time is a critical measure since the fast simulation
algorithm is offered on the internet and the typical
simulation times of a comprehensive simulation like
Polysun (18 seconds on a 2.2 GHz i7 CPU with Windows
7) is already too long. The Sunny Design code evaluates
in 90 miliseconds and the speed-up therefore is a factor
200.
4.
ACKNOWLEDGEMENT
CONCLUSION AND OUTLOOK
PV self-consumption in combination with heat pumps is
a good way to reduce the load on the distribution power
grid. However the pulsed operation of the heat pumps in
reality naturally puts an upper limit to the selfconsumption ratio.
In order to obtain a good match between the PV
installation and the heat pump, the entire system
dynamics has to be considered. They need to match both
in the power levels as well as in the energy balance.
There are many approaches to PV self-consumption
calculation and this work aims to give some indication to
rate these calculations. In order to propose a quick
algorithm, one might be tempted to use a one hour time
step or even an algorithm that calculates selfconsumption on a daily or monthly basis. However, it has
been found that this is not accurate enough and at least a
five minute time step should be used, otherwise the
electrical consumption profiles and the pulsed operation
of the heat pump cannot be modeled adequately.
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