MCE- MODELS
DEVELOPMENT OF MARGINAL CONVERSION
EFFICIENCY MODELS FOR POWERTRADE
Göran Smith
Tommy Fransson
1.
SUMMARY
Powertrade is a distributed model based optimization methodology under development at AB Volvo that intends to include all energy consumers and energy storages in a single vehicle energy
management strategy. The objective is to maximize global efficiency and thereby lower the total net energy losses that contribute to the total fuel cost.
The scope of the project that this report is a part of is to develop Powertrade for demonstration in a parallel-hybrid city bus. Viktoria Swedish ICT has during the project assisted AB Volvo by modeling marginal conversion efficiency for the components that are included in the current version of
Powertrade. This report describes the development of these models and the reasoning behind them. Models were developed for the following components; internal combustion engine, electric machine, air conditioning system, DC/DC converter, 600-volt battery and 24-volt battery. The suitability of the models differed profoundly, mainly due to that some models were based on unsatisfactory
measurement data, but also since the components differ in nature and complexity. The overall conclusion is that all MCE-models but AC and 24-volt are sufficient for verifying the Powertrade’s ability to handle different variants of vehicles and to indicate the effort required for a production ready implementation. Significant model refinement is however needed if for example the concept’s savings potential is to be evaluated.
2. INTRODUCTION
2.1.
BACKGROUND
Auxiliaries contribute to a substantial part of vehicles’ total energy consumption and the potential for reduction of this consumption have gained attention during recent years. Volvo is consequently seeking new measures on how to optimize the utilization of all energy users and thereby minimize their impact on fuel economy.
Powertrade is a distributed model based optimization methodology under development at AB Volvo that aims to include all energy consumers and energy storages in a single vehicle energy
management strategy. The objective is to maximize global efficiency and thereby lower the total net energy losses that contribute to the total fuel cost. The methodology has been under development since 2010 and has undergone a few major revisions. Its feasibility has been tested in several simulations and during real usage in a conventional distribution truck, indicating promising potential. The scope of the project that this report is a part of is to develop Powertrade for demonstration in a parallel-hybrid city bus. The main goals with the demonstration are to;
1. Develop the models that are required for further development 2. Verify the concepts ability to handle different variants of vehicles 3. Indicate the effort required for a production ready implementation
The research institute Viktoria Swedish ICT has during the project used existing component models and data sets to develop marginal conversion efficiency models to be used in the present version of Powertrade. This report describes the development of these models and the reasoning behind them.
2.2.
POWERTRADE METHODOLOGY
The main idea behind the Powertrade methodology is to use microeconomic models with producers and consumers that interact with energy markets where quantities of power are traded. Each component in the algorithm acts to maximize its profit and/or maximize its utility, resulting in supply and demand curves handed to the markets. Global equilibrium is then achieved via a Walrasian auction-like process1 that determines market-clearing prices2. The prices regulate the quantities of energy supplied to the components and these quantities are ultimately realized through control actions applied to the power converters.
Identified advantages with Powertrade compared to other methods for energy management are among other things;
1. Enhanced understanding and eased communication due to that the methodology can be described in economical terms
2. Potential to remain highly modular
3. Small CPU demand and memory footprint
2.3.
POWERTRADE COMPONENTS
Any component or system that provide or receive power is a potential part of Powertrade. These components interact in Powertrade via so called markets. Markets are in this report defined as follows;
A market is a price decider that based on information on supply and demand of a certain form of power determines the market-clearing price of that form of power.
Components that interact with a specific market are in Powertrade categorized as either producers or consumers of the type of power that is traded on the market. Both producers and consumers are however in a wider perspective actually converters since all components convert power from one form to another. Many components also interact with several markets and should subsequently be defined differently depending on which market that is in focus. Some components moreover have storage
1 A Walrasian auction is a concurrent auction where agents compute their demand for the traded good at every
possible price and submits this to the Walrasian auctioneer. The auctioneer then matches total demand and total supply and finds a market-clearing price (Walrasian market equilibrium). About.com
2 A market-clearing price is that price of a good at which the market clears. Quantity supplied is equal to quantity
capacity, i.e. an internal market. In this report components are therefore defined as either converters or buffers that can act as either producer or consumers.
A converter is a component that has ability to transform power from one form to another A buffer is a converter that also has flexible power demand and can store energy in some form
A component act as produces when it delivers power to a market A component act as consumer when it consumes power from a market
Since power conservation must hold, the following is true for every component within Powertrade; 𝑄!− 𝑄!− 𝑄!− 𝑄!= 0
𝑄!= 𝑅𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝑝𝑜𝑤𝑒𝑟, 𝑄!= 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑 𝑝𝑜𝑤𝑒𝑟, 𝑄!= 𝐷𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑 𝑝𝑜𝑤𝑒𝑟
𝑎𝑛𝑑 𝑄!= 𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑠𝑡𝑜𝑟𝑒𝑑 𝑒𝑛𝑒𝑟𝑔𝑦3
2.4.
MARGINAL CONVERSION EFFICIENCY
Marginal conversion efficiency (hereinafter referred to as MCE) is defined as the limit of the
incremental efficiency when adding an additional quantity of output to a component, as the quantity tends to zero. It is in other words the derivative of good as function of work or the inverse of the derivative of work as function of good;
𝜁 𝑄!""# =
𝑑𝑄!""#
𝑑𝑄!"#$ 𝑜𝑟 𝜁 𝑄!"#$ =
1 𝑑𝑄!"#$ 𝑑𝑄!""#
MCEs are key for the Powertrade algorithm since they enable translation of market supply and market demand curves to supply and demand curves for components.
For a component producing Q2 (Figure 2-1), the relation between its supply curve (S(Q2)) and the market supply curve for the market that it receives power from (dCost/dQ1) is calculated along the following logics; 𝑆 𝑄! = 𝑑𝐶𝑜𝑠𝑡 𝑑𝑄! = 𝑑𝐶𝑜𝑠𝑡 𝑑𝑄! 𝑑𝑄! 𝑑𝑄!= 𝑑𝐶𝑜𝑠𝑡 𝑑𝑄! 1 𝜁 𝑄!
Figure 2-1 A general component's interaction with markets
Similarly, for a component consuming Q1 (Figure 2-1), the relation between its demand curve (D(Q1)) and the market demand curve for the market it delivers power to (dUtility/dQ2) is calculated along the following logics; 𝐷 𝑄! = 𝑑𝑈𝑡𝑖𝑙𝑖𝑡𝑦 𝑑𝑄! = 𝑑𝑈𝑡𝑖𝑙𝑖𝑡𝑦 𝑑𝑄! 𝑑𝑄! 𝑑𝑄!= 𝑑𝑈𝑡𝑖𝑙𝑖𝑡𝑦 𝑑𝑄! 𝜁 𝑄!
As seen above, it is convenient to have MCE as an expression of delivered power when components act as producers and as an expression of received power when they act as consumers.
2.5.
METHOD FOR MODEL DEVELOPMENT
To model the relations for marginal conversion efficiencies, the first step has in this project been to approximate a continuous and monotone relation between good and work, with either delivered or received power as base. This approach precludes local extreme points and enables localization of global maximum for efficiency. The project has moreover only examined quadratic approximations even though that isn’t a requirement in the Powertrade algorithm.
𝑄! 𝑄! = 𝐴!𝑄!!+ 𝐵
!𝑄!+ 𝐶! 𝑓𝑜𝑟 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑒𝑟𝑠 𝑎𝑐𝑡𝑖𝑛𝑔 𝑎𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟𝑠 (𝑄!= 𝑤𝑜𝑟𝑘, 𝑄!= 𝑔𝑜𝑜𝑑)
𝑄! 𝑄! = 𝐴!𝑄!!+ 𝐵!𝑄!+ 𝐶! 𝑓𝑜𝑟 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑒𝑟𝑠 𝑎𝑐𝑡𝑖𝑛𝑔 𝑎𝑠 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟𝑠 𝑄!= 𝑤𝑜𝑟𝑘, 𝑄!= 𝑔𝑜𝑜𝑑
𝑄! 𝑄! = 𝐴!𝑄!!+ 𝐵!𝑄!+ 𝐶! 𝑓𝑜𝑟 𝑏𝑢𝑓𝑓𝑒𝑟𝑠 𝑎𝑐𝑡𝑖𝑛𝑔 𝑎𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟𝑠 (𝑄!= 𝑤𝑜𝑟𝑘, 𝑄!= 𝑔𝑜𝑜𝑑)
𝑄! 𝑄! = 𝐴!𝑄!!+ 𝐵!𝑄!+ 𝐶! 𝑓𝑜𝑟 𝑏𝑢𝑓𝑓𝑒𝑟𝑠 𝑎𝑐𝑡𝑖𝑛𝑔 𝑎𝑠 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟𝑠 𝑄!= 𝑤𝑜𝑟𝑘, 𝑄!= 𝑔𝑜𝑜𝑑
The polynomal curve fitting matlab tool polyfit has been used to perform the approximations. In matlab, the script p=polyfit(x,y,n) finds the coefficients of a polynomial p(x) of degree n that fits the data, p(x(i)) to y(i), in a least squares sense. The result p is a row vector of length n+1 containing the polynomial coefficients in descending powers;
𝑝 𝑥 = 𝑝!𝑥!+ 𝑝!𝑥!!!+. . +𝑝!𝑥 + 𝑝!!!
What data for good and work approximates have been based on and how the data has been produced has varied. Partly due to the differences in nature between the different components but mostly due to what measurement data and simulation models that have been available. This will be further
discussed in the chapter “Development of models”. The approximated relations have however subsequently been derived in order to create expressions for marginal conversion efficiencies;
𝜁 𝑄! = 1 𝑑𝑄! 𝑄! 𝑑𝑄!= 1 2𝐴!𝑄!+ 𝐵! 𝑓𝑜𝑟 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑒𝑟𝑠 𝑎𝑐𝑡𝑖𝑛𝑔 𝑎𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟𝑠 𝜁 𝑄! = 𝑑𝑄! 𝑄! 𝑑𝑄! = 2𝐴!𝑄!+ 𝐵! 𝑓𝑜𝑟 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑒𝑟𝑠 𝑎𝑐𝑡𝑖𝑛𝑔 𝑎𝑠 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟𝑠 𝜁 𝑄! = 1 𝑑𝑄! 𝑄! 𝑑𝑄!= 1 2𝐴!𝑄!+ 𝐵! 𝑓𝑜𝑟 𝑏𝑢𝑓𝑓𝑒𝑟𝑠 𝑎𝑐𝑡𝑖𝑛𝑔 𝑎𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟𝑠 𝜁 𝑄! =𝑑𝑄! 𝑄! 𝑑𝑄! = 2𝐴!𝑄!+ 𝐵! 𝑓𝑜𝑟 𝑏𝑢𝑓𝑓𝑒𝑟𝑠 𝑎𝑐𝑡𝑖𝑛𝑔 𝑎𝑠 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟𝑠
The expressions for MCE have thereafter been implemented in the Powertrade algorithm in form of Simulink models.
3.
DEVELOPMENT OF MODELS
3.1.
ELECTRIC MACHINE
3.1.1. Background information
Component info: 180-kW permanent magnet synchronous electric machine developed by Remy. An efficiency map from Volvo AB (d_em_pmsm_remy_180kW_420Nm.m) for the electric machine was used as input to the Powertrade model (see Figure 3-1). Additionally a fixed efficiency of the inverter was stated to 97%.
Figure 3-1 Initial efficiency map for the 180kW permanent magnet synchronous electric machine from Remy
3.1.2. Development of model
The input data in Figure 3-1 was on the form of efficiency as function of torque and angular velocity. Using the relationship between power, torque, angular velocity and efficiency below it’s possible to transform the efficiency map into a relationship between electric power and mechanical power. The end result is visible in Figure 3-2.
𝑃!"!#$%&#'"= η 𝜔, 𝜏 𝑃!"#!!"#$!% ⇒ 𝑃!"#!!"#$!% = 𝜏𝜔 = 𝜏2𝜋𝑅𝑃𝑀 60 ⇒ 𝑃!"!#$%&#'"= η 𝜔, 𝜏 𝜏2𝜋𝑅𝑃𝑀 60 0 2000 4000 6000 8000 10000 12000 −500 −400 −300 −200 −100 0 100 200 300 400 500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Angular velocity (RPM) Input data − Efficiency as a function of torque and angular velocity
Torque(Nm)
Figure 3-2 Electric power as function of mechanical power and angular velocity
Due to non-negligible inertia in the system, in combination with a fast update frequency, it was deemed reasonable to assume that the angular velocity in every time step could be considered constant. By making this assumption it was possible to parameterize the function based on the angular velocity. A simple second order one-dimensional polynomial fitting was then applied to each angular velocity step in order to create the Powertrade model (Figure 3-3). Since good equals the mechanical power (Q2) and work the electric power (Q1) for the electric machine, MCE is the derivative of the model.
Figure 3-3 Model of electric power as function of mechanical power and angular velocity
0 2000 4000 6000 8000 10000 12000 −6 −4 −2 0 2 4 6 x 105 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 x 105 Angular velocity (rpm) Electrical power as function of mechanical power − edge of working area removed
Mechanical power (W) Electrical power (W) 0 2000 4000 6000 8000 10000 12000 −6 −4 −2 0 2 4 6 x 105 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 x 105 Angular velocity (rpm) Model of electrical power as function of mechanical power
Mechanical power (W)
3.1.3. Reflections
The transform from torque to energy introduces ’fuzziness’ on the edge between the area where the efficiency is defined and the area where it isn’t. A higher quality edge is expected if upsampling and perhaps also extrapolating the area before performing the transform, and then afterwards downsample and trimming the edge. This likely impacts the complete over-all quality of the model because
’fuzziness’ from the edges makes an impact on the overall approximations - which is visible as a ‘wave pattern’ in Figure 3-3.
The model was made from several one-dimensional approximations over both the positive and negative power range. The rationale behind this was the predicted low available computing power in combination with a decision that the error was deemed sufficiently small despite using this approach. A better approach would be to divide the working area into at least positive and negative energy flows. Additionally a two-dimensionally approach could be used to perhaps improve the quality even further.
3.2.
INTERNAL COMBUSTION ENGINE
3.2.1. Background information
An efficiency map (T-data) for the combustion engine and a max torque map
(mt_MAX_TORQUE_HIGH_MAP_y) were used to describe engine P3661 240H (Engine type: d_engplnt_wh_all_d5k240eu6_BC).
3.2.2. Development of model
The internal combustion engine is a converter that transforms chemical energy from the fuel tank to mechanical power at the crankshaft. MCE was defined as a function of received power, i.e. diesel intake.
The output from the efficiency map (T-data) is the diesel mass flow quantity of the internal combustion engine per engine stroke. By extending the matrix it was possible to get mass flow per second.
𝑚! 𝜔, 𝑇 = 𝑇𝑑𝑎𝑡𝑎 𝑚𝑔 𝑠𝑡𝑟𝑜𝑘𝑒 ⇒ 𝑚 𝜔, 𝑇 = 𝑇𝑑𝑎𝑡𝑎 𝜔(𝑛𝑜. 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟𝑠) 120 ∗ 10! 𝑘𝑔 𝑠
Hence, the extended matrix represented mass flow per second as a function of angular velocity and torque. By using polynomial fitting in two steps on the data and a max torque curve as upper boundary condition, an approximation for the relation was established.
𝑚 𝜔, 𝑇 = 𝑎 𝜔 𝑇!+ 𝑏 𝜔 𝑇 + 𝑐 𝜔 𝑘𝑔
𝑠 𝑖𝑛 𝑤ℎ𝑖𝑐ℎ 𝑎 𝜔 = 𝑎!𝜔!+ 𝑎
!𝜔 + 𝑎!, 𝑏 𝜔 = 𝑏!𝜔!+ 𝑏!𝜔 + 𝑏! 𝑎𝑛𝑑 𝑐 𝜔 = 𝑐!𝜔!+ 𝑐!𝜔 + 𝑐!
The fit of the approximation can be discerned in the figures below (Figure 3-4 visualizing the data points and Figure 3-5 visualizing the approximation).
Figure 3-4 Tdata data points
Figure 3-5 Approximation
That approximation was subsequently extended to form an expression for delivered power as function of received power. 𝑚 𝜔, 𝑇 = 𝑎 𝜔 𝑇!+ 𝑏 𝜔 𝑇 + 𝑐 𝜔 𝑘𝑔 𝑠 ⇔ 𝑄! 𝜔, 𝑇 = 𝑎 𝜔 𝑇!+ 𝑏 𝜔 𝑇 + 𝑐 𝜔 𝑢 𝑊 ⇔ 𝑄! 𝜔, 𝑇 = 𝑎 𝜔 𝑄!! 𝜔! + 𝑏 𝜔 𝑄! 𝜔 + 𝑐 𝜔 𝑢 𝑊
Finally, this equation was derived and the relation between MCE and delivered power to the auxiliaries was established. 𝜁!"# 𝑄! =𝑑𝑄! 𝑑𝑄! = 1 𝑑𝑄! 𝑑𝑄! = 𝜔 𝑢 2𝑎 𝜔 𝑄! 𝜔 + 𝑏 𝜔 −
The final outcome, i.e. how the model estimates that MCE varies with angular speed and torque can be seen in Figure 3-6.
Figure 3-6 MCE for the internal combustion engine 3.2.3. Reflections
The temperature of air, humidity of air and barometric pressure affect the internal combustion engine’s performance. Especially barometric pressure and ambient temperature has been identified as highly influential.4 Higher atmospheric pressures increase the air density and, therefore, augment the intake air charge to the engine while ambient temperature among other things is found to affect the flame speed, the combustion reaction rate, the uniformity of the fuel-air mixture, the volumetric efficiency and the heat transfer rate though the cylinder walls. Atmospheric conditions are however not considered in the efficiency map and these variances are therefore not reflected in the MCE model. A suggestion for future improvement is thus to include a correction factor for varying atmospheric conditions. The model is however in its current embodiment sufficient for its purpose (i.e. verify Powertrade’s ability to handle different variants of vehicles and indicate the effort required for a production ready
implementation).
3.3.
DC/DC CONVERTOR
3.3.1. Background information
Data for the DC/DC converter currently in production was taken from the document 1P135731 - DCDC efficiency.pdf, which summarizes a test called Box-build test Eu6 P23 S/N: 00402546. In the test, delivered voltage was set to 28v while received voltage and delivered current was varied. The consequential received current was measured in the test, which generated nine data points for the relation between received and delivered power (Figure 3-7).
VARIABLES 1 2 3
Delivered voltage [V] 28 28 28
obviously a converter and therefore treated as such. MCE is moreover defined as a function of the delivered power since the DC/DC convertor affects the price of the low-voltage market much more than the price of the high-voltage market. Connected to the low-voltage market, the DC/DC convertor is moreover the only controllable component and thus the only component that can be managed in order to influence the price. On the high voltage market on the other hand, the influence of the DC/DC convertor is almost negligible in comparison with for example the influence of the electric motor. A curve for received power as a function of delivered power was therefore fitted to the data points and MCE derived from it.
𝑄! 𝑄! = 𝐴𝑄!!+ 𝐵𝑄!+ 𝐶 ⇔ 𝑄! 𝑄! = 𝐴 𝐼!𝑉! !+ 𝐵 𝐼!𝑉! + 𝐶 𝜁!"!" 𝑄! = 1 𝑑𝑄! 𝑄! 𝑑𝑄!= 1 𝑑 𝐴𝑄!!+ 𝐵𝑄!+ 𝐶 𝑑𝑄! = 1 2𝐴𝑄!+ 𝐵= 1 2𝐴𝐼!𝑉!+ 𝐵
The curve for received power as a function of delivered power, which was fitted to the nine data points, had a least square value of 1.00, indicating a more or less perfect fit (Figure 3-8).
Figure 3-8 Data points and approximated curve How MCE varies upon delivered power can be seen in Figure 3-9.
Figure 3-9 MCE for DC/DC converter 3.3.3. Reflections
The model seems good enough for verifying the ability to handle different variants of vehicles and to indicate the effort required for a production ready implementation.
3.4.
AIR CONDITIONING SYSTEM
3.4.1. Background information
The test bus, that this version of Powertrade is developed for, utilizes two series connected Citysphere units (a master and a slave) for cooling the passenger cabin. These units receive power from the 24v-alternator and/or the DC/DC converter and are managed by an internal control system developed by the manufacturer Spheros. The driver can however adjust the following settings via a control panel; on/off, fan speed and nominal temperature difference (target value for the cabin temperature as function of the ambient temperature).
Operating conditions for the air conditioning are; - Vehicle motor is running
- Ambient temperature is higher than 17C - Cabin temperature is higher than 22C
- Cabin temperature is higher than ambient temperature minus the nominal difference set by the driver (standard is 3C)
Each unit consumes 72 ampere (compressor motor 55A, condenser fan, 10A and compressor fan 7A) and has a cooling capacity around 3.8kW5 and an airflow rate around 1’350m3/h.6
The citysphere air conditioning system was however replaced when Volvo upgraded their city buses to Euro-6 standard. The new city buses will utilize Spheros newer air conditioning system Revo-E. 3.4.2. Development of model
𝑝!= 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑝𝑜𝑤𝑒𝑟 𝑊
𝑝!= ∆𝑄𝑚!"#$= 𝑚!"#$− 𝑚!"#$!# 𝑇!"#+ 𝑚!"#$!#𝑇!"# − 𝑇!"#!!"#𝑚!"#! 𝑐 𝑊
Figure 3-10 Model of a general air conditioning system
Volvo provided a basic model (ac_bus_std.mdl) that simulates the temperature in a passenger cabin based on the work of an AC-system. The temperature of the air coming out of the AC (Tevap_out) is in the model estimated via interpolation and the cabin temperature is then updated based on the evaporator’s mass flow and several constants that describe the cabin environment. The interpolation, which also estimates the compressor’s power consumption, is based on a data set with measured values (SSM_AC_Bus_FK40_560). Air temperatures coming into condenser and evaporator, relative humidity, mass flows and the compressor speed were used as input values when developing the data. The variables were varied as described in Figure 3-11 when executing the measurements, generating 4375 data points in total;
VARIABLES 1 2 3 4 5 6 7
Compressor speed [rpm] 500 1000 1500 2000 2500 3000 3500
Condenser temp (in) [C] 20 25 30 35 40
Condenser mass flow [kg/s] 0.5 1 1.5 2 3
Evaporator temp (in) [C] 15 20 25 30 35
Evaporator mass flow [kg/s] 0.5 1 1.5 2 3
Relative humidity [%] 30
Figure 3-11 Input to measurement of interpolation data
Power consumptions of condenser and evaporator fans are not considered in the model and mass flows are treated as independent constants. Another notable property of the model is that the
compressor speed is directly related to the engine speed, as it is in most conventional vehicles. This is however not the case for the hybrid bus. The model thereby had to be adjusted in order to represent an AC that is powered by the 24v-alternator. To do this, the interpolation process was reorganized so that power supply was used as input value instead of compressor speed. It was thus possible to generate values for good and work by varying ambient temperature (equals evaporator temperature (in) since recirculation was set to zero) and power supply and simulating the resulting evaporator temperature (out)7. Since values for neither Citysphere, nor Revo-E were available, the original data set had to be used. The magnitude of power consumption was moreover significantly enlarged (from maximum levels around 3kW to 30kW) since that is the level that buses normally experience, according to Volvo’s project leader’s experience.
The outcome of the simulation was poor, not showing any understandable pattern. It is for example rational to expect that increased work never should result in decreasing good, which it sometimes do according to the simulation result. Due to these data points, it was impossible to accomplish a
reasonable curve fit by using polyfit. Instead, in order to at least develop something to test in the Powertrade algorithm, three points from each simulation were picked out (Figure 3-12), and curves fitted to these points (Figure 3-13). The model for MCE was subsequently derived from the curve expressions (Figure 3-14).
P2 UPON amb_temp AND P1 P1 = 5kW P1 = 15kW P1 = 30kW
Amb_temp = 17C P2 = 18kW P2 = 25kW P2 = 30kW Amb_temp = 20C P2 = 23kW P2 = 30kW P2 = 32kW Amb_temp = 23C P2 = 25kW P2 = 31kW P2 = 32kW Amb_temp = 26C P2 = 33kW P2 = 35kW P2 = 36kW Amb_temp = 29C P2 = 38kW P2 = 40kW P2 = 41kW Amb_temp = 32C P2 = 40kW P2 = 42kW P2 = 43kW Amb_temp = 35C P2 = 42kW P2 = 45kW P2 = 46kW
Figure 3-12 Identified points which curves were fitted to
Figure 3-14 MCE for air conditioning system 3.4.3. Reflections
Absence of both a capable model and accurate data for the correct component made it impossible to develop a sufficient model for the AC’s MCE. For enabling development of such a model, data for the addressed AC (in this case Citysphere) needs to be produced and it must be possible to describe the data as a polynomial equation. Whether this is possible or not cannot be determined from the
performed work due to the condition of the existing data set. New data should preferably include more relevant factors than the current such as ambient humidity, vehicle speed and the interplay between compressor and fans. When developing the data, triggers and consequences should moreover be the same as in the AC’s control strategy (power supply should for example be varied and not engine speed). Finally, in order to enable inclusion of the model in an actual bus, a communication interface between Powertrade and the AC must be set up. This interface will look different depending on which AC is addressed. Close collaboration with the manufacturer is thereby desirable in order to make the process of producing accurate data and developing a control strategy efficient.
To sum up; the development of the model helped indicating the effort for a production ready implementation but isn’t sufficient for verifying Powertrade’s ability to handle different variants of vehicles in its current shape.
3.5.
600-VOLT BATTERY
3.5.1. Background information
A model for the battery currently used in Volvos hybrid production described by the following files was used as input for the MCE model development.
• d_bat_lithiumIon_A123_5690Wh.m • d_cell_lithiumion_A123_4Ah4.m • d_ess_lithiumion_A123_5690Wh.m • d_bmu_lithiumion_A123_5690Wh.m 3.5.2. Development of model
The 600-volt battery is an energy buffer since it has a flexible power demand and can store power. It acts furthermore both as producer and consumer in Powertrade. MCE was as a consequence defined differently depending on if the battery is receiving or delivering power. MCE equals the second derivative of stored energy as a function of received power when the battery acts as a consumer. When the battery acts as producer, MCE is instead equal to the second derivative of delivered power as a function of stored energy.
𝜁!"## 𝑄! = 1 𝑑𝑄! 𝑄! 𝑑𝑄!= 1 2𝐴!𝑄!+ 𝐵! 𝑤ℎ𝑒𝑛 𝑎𝑐𝑡𝑖𝑛𝑔 𝑎𝑠 𝑎 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 (𝑖 < 0) 𝜁!"## 𝑄! = 𝑑𝑄! 𝑄! 𝑑𝑄! = 2𝐴!𝑄!+ 𝐵! 𝑤ℎ𝑒𝑛 𝑎𝑐𝑡𝑖𝑛𝑔 𝑎𝑠 𝑎 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 (𝑖 > 0)
AB Volvo provided a standard simulink model for batteries (ess.std.mdl) and data on cell temperature, state of charge, voltage and current from a standard urban drive cycle8. It was at an early stage found that the voltage drop due to the battery’s internal resistance caused more than 99% of the battery’s energy losses. Other loss sources included in the standard battery model were therefore neglected and the model was simplified.
The internal voltage drop is a result of ohmic and dynamic resistance (Figure 3-15). The equation for the ohmic resistance is quite simple while the dynamic resistance state is more complex in its nature.
𝑂ℎ𝑚𝑖𝑐 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑑𝑟𝑜𝑝 = 𝑖 𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑜𝑟 𝑟𝑒𝑠. +𝑐𝑒𝑙𝑙𝑡𝑜𝑐𝑒𝑙𝑙𝑏𝑢𝑠𝑏𝑎𝑟 𝑟𝑒𝑠. +𝑖𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑜ℎ𝑚𝑖𝑐 𝑟𝑒𝑠. 𝑆𝑜𝐶, 𝑇 𝐷𝑦𝑛𝑎𝑚𝑖𝑐 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑑𝑟𝑜𝑝 = 𝑓!(𝑆𝑜𝐶, 𝑇, 𝑖, 𝑓!!!)
Figure 3-15 Generalization of a battery
Since both ohmic and dynamic resistances contribute significantly to the voltage drop (Figure 3-16), the model ought to take both resistances into account, and since the dynamic losses is reliant on the amount of energy stored in the capacitor (Figure 3-15)9, the model should preferably be dependent on the state of the capacitor (i.e. upon past current). The last requirement was however not feasible to meet in this version of Powertrade. The capacitor’s degree of charge is not available on the CAN-network and to store the information in the algorithm itself might oblige a memory footprint too large for the equipment meant to be used for implementation in the test vehicle.
Figure 3-16 Voltage drop during a standard urban drive cycle
Values for the constants needed for the MCE equations (A1, B1, A2 and B2) were instead developed by modifying the battery model and simulating the drive cycle that was provided by AB Volvo. In other words, the resulting sum of dynamic and ohmic loses was simulated upon the drive cycle values for state of charge, current and temperature.
The simulation resulted in 12’628 data points. They were divided upon temperature (26-28C, 28-30C), state of charge (33.6-44.8%, 44.8-50.0%, 50.0-55.4%, 55.4-61.6%) and whether the battery acted as a consumer or as a producer. This generated 16 sets of data. Quadratic curves were fitted to these sets (Figure 3-17) and the derivatives formed the relations for MCE (Figure 3-18).
Figure 3-18 MCE for 600-volt battery
3.5.3. Reflections
Since the state of the capacitor is not included in the state dependency, the developed model’s estimate of the internal dynamic voltage drop will correspond to the average capacitor state during comparable states during the supplied drive cycle. The accuracy of the model is therefore partly determined by how similar the performed drive cycle is to the test drive cycle. The anticipation is that the simulated drive cycle is fairly similar to the drive cycle the test vehicle is supposed to perform and that the level of inaccuracy therefore will be limited during the test. The model must nevertheless be refined in order to ensure accurate estimates independent of drive cycle choice. It’s recommended to include the state of the capacitor in the state dependency. This requires logging of the currents going in and out from the battery.
All things considered, the established model indicates the effort required for a production ready implementation. To verify Powertrade’s ability to handle different variants of vehicles it must be further developed.
3.6.
24-VOLT BATTERY
3.6.1. Background information
The 24V battery may be used as an energy buffer and is described by the model; • D_bat_leadacid_24V225Ah.m
• D_cell_leadacid.m • Pba_battery_param.mat 3.6.2. Development of model
The 24-volt battery is from a Powertrade perspective fundamentally quite similar to its 600-volt counterpart. It is an energy buffer that acts both as producer and consumer. Measurement data from drive cycles such as for the 600-volt battery were however not available for the 24-volt battery and many parameters needed for operating the standard battery model were missing. Thus, it was at the time impossible to for example compare the influence from dynamic and ohmic resistance on the
Figure 3-19 Internal ohmic resistance
After contact with battery experts at AB Volvo, it was decided to await better data from new tests that were being performed at that time. In the meantime, a temporary model only including losses due to the internal ohmic resistance was developed. The new data did however never arrive, the issue fell into oblivion and a new model was never developed during the project.
The temporary model was developed by altering current, state of charge and temperature and simulating the consequential delivered, stored and received power (Figure 3-20).
VARIABLES 1 2 3 4 5
Current (to battery) [A] -300 -299 .. 299 300
State of charge [-] 0 10 .. 90 100
Temperature [C] -20 -10 .. 30 40
Figure 3-20 Input to simulation
This resulted in 46277 data points sorted into 22 different groups. Curves were fitted to the data points of each group and expressions for MCE derived from them (Figure 3-21 and Fel! Hittar inte
referenskälla.Figure 3-22).
Figure 3-22 MCE for 24-volt battery when acting as producer 3.6.3. Reflections
Accurate measurement data and battery parameters are needed in order to develop an appropriate model for the 24-volt battery. The current version doesn’t consider the whole voltage drop and is also based on dubious data. It is thus insufficient both for verifying Powertrade´s ability to handle different types of vehicles and for indicating required effort for a production ready implementation. A model to be implemented in a test vehicle should also utilize fewer than 22 groups in order to minimize the memory footprint.
4. CONCLUSIONS
There are, as mentioned earlier in the report, three main goals with demonstrating Powertrade in a parallel-hybrid city bus;
1. Develop the models that are required for further development 2. Verify the concepts ability to handle different variants of vehicles 3. Indicate the effort required for a production ready implementation
The work that this report describes focused on the first question but has also generated some input to the two other questions.
1. Develop the models that are required for further development
MCE models for DC/DC-converter, internal combustion engine and electric machine are suitable for to be used in the Powertrade algorithm. The AC model and the battery models need on the other hand further refinement in order to allow the next steps in the development of the concept, i.e. road test or relevant evaluation of saving potential.
2. Verify the concepts ability to handle different variants of vehicles
The ability to handle different variants of vehicles can of course not be determined by evaluating the development of models alone, but should rather be resolved by assessing the entire procedure of adjusting Powertrade. The only thing that suggests that it would be more difficult to develop MCE models for hybrid vehicles than for conventional vehicles is that the algorithm for hybrids should
include more components. The risk for facing a component difficult to model is thereof naturally higher. 3. Indicate the effort required for a production ready implementation
Again, this question has a wider scope and cannot be fully appraised by only evaluating the developments of models. The effort required for developing production ready MCE models has however been identified as significant but workable. Main hinders (beyond organizational issues) that complicates the process are;
- Lack of a recognized practice on how to develop MCE models - Lack of access to required component data
- Lack of information available on CAN-network
- Lack of obvious methods for controlling components that aren’t integrated in current control strategies
5. FUTURE WORK
The following activities are suggested in order to improve the MCE models and thereby strengthen the Powertrade concept;
- Develop a methodology for how to include new components into Powertrade. This could for example materialize in form of;
o A cheat sheet describing the model development process o Well documented software for creating new models o API specifications
o Specifications of component information needed in order to build models
- Verify the methodology used during this project by applying it on other versions of the same type of components.
- Produce interpolation data for any of the AC-systems that are utilized by AB Volvo’s city buses. This is a requirement for enabling development of a relevant AC-model that represents the equipment on the buses. The manufacturer Spheros could be involved in the development to facilitate a cost-effective process. The interpolation should preferably also include more variables than in the current case (e.g. humidity).
- Develop a control interface for the AC-system together with the manufacturer Spheros. This is needed in order to actively involve the AC in the algorithm.
- Develop a new model for the 600-volt battery that includes capacitor state in the state dependency. This would facilitate accuracy on drive cycles dissimilar to the drive cycle used when developing the model
