Buildings.Fluid.Movers.BaseClasses.Characteristics

Information

This package implements performance curves for fans and pumps.

The following performance curves are implemented:

 dp =f(V_flow, r_N, {V_flow_nominal, dp_nominal})
 P  =f(V_flow, r_N, {V_flow_nominal, dp_nominal})
 eta=f(r_V,         {r_V_nominal, eta_nominal})

The package is similar to Modelica.Fluid.Machines.BaseClasses.PumpCharacteristics, with the following exceptions:

• Instead of head in meters H20, total pressure in Pascal is used. This makes the models applicable for fans as well since the flow models from Modelica.Fluid use the density of the medium model, such as the density of air instead of water, to convert head to pressure.
• In Modelica.Fluid.Machines.BaseClasses.PumpCharacteristics, input to the functions is V_flow/r_N, where r_N=N/N_nominal, and the mover model computes, for example for a quadratic performance curve,

    dp = r_N^2 * f(V_flow/r_N) 
       = r_N^2 * ( c1 + c2 * V_flow/r_N + c3 * (V_flow/r_N)^2) 
       = r_N^2 * c1 + r_N * c2 * V_flow + c3 * V_flow^2.
  

  Since f(V_flow/r_N) = c1 + c2 * V_flow/r_N + c3 * (V_flow/r_N)^2 is singular for r_N=0, we redefined this function as dp = f(V_flow, r_N) = r_N^2 * c1 + r_N * c2 * V_flow + c3 * V_flow^2 which allows computing dp for r_N=0. Note, however, that the model of the Buildings library, as well as the model of Modelica.Fluid, is still singular for r_N=0 for performance curves that have a higher order than 2.
• This package also contains higher order functions for power consumption and efficiency.

Package Content

Name	Description
baseFlow	Base class for fan or pump flow characteristics
basePower	Base class for fan or pump power consumption characteristics
baseEfficiency	Base class for efficiency characteristics
linearFlow	Linear flow characteristic
quadraticFlow	Quadratic flow characteristic
polynomialFlow	Polynomial flow characteristic
linearPower	Linear power consumption characteristic
quadraticPower	Quadratic power consumption characteristic
polynomialPower	Polynomial power consumption characteristic
constantEfficiency	Constant efficiency characteristic
linearEfficiency	Linear efficiency characteristic
quadraticEfficiency	Quadratic efficiency characteristic
polynomialEfficiency	Polynomial efficiency characteristic
solve	Wrapper for Modelica.Math.Matrices.solve
der_solve	Derivative for function solve
Examples	Examples to test implementation of derivative function

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.baseFlow

Base class for fan or pump flow characteristics

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type	Name	Default	Description
VolumeFlowRate	V_flow		Volumetric flow rate [m3/s]
Real	r_N		Relative revolution, r_N=N/N_nominal [1]

Outputs

Type	Name	Description
Pressure	dp	Fan or pump total pressure [Pa]

Modelica definition

partial function baseFlow 
  "Base class for fan or pump flow characteristics"
  extends Modelica.Icons.Function;
  input Modelica.SIunits.VolumeFlowRate V_flow "Volumetric flow rate";
  input Real r_N(unit="1") "Relative revolution, r_N=N/N_nominal";
  output Modelica.SIunits.Pressure dp(min=0, displayUnit="Pa") 
    "Fan or pump total pressure";
end baseFlow;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.basePower

Base class for fan or pump power consumption characteristics

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type	Name	Default	Description
VolumeFlowRate	V_flow		Volumetric flow rate [m3/s]
Real	r_N		Relative revolution, r_N=N/N_nominal [1]

Outputs

Type	Name	Description
Power	consumption	Power consumption [W]

Modelica definition

partial function basePower 
  "Base class for fan or pump power consumption characteristics"
  extends Modelica.Icons.Function;
  input Modelica.SIunits.VolumeFlowRate V_flow "Volumetric flow rate";
  input Real r_N(unit="1") "Relative revolution, r_N=N/N_nominal";
  output Modelica.SIunits.Power consumption "Power consumption";
end basePower;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.baseEfficiency

Base class for efficiency characteristics

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type	Name	Default	Description
Real	r_V		Volumetric flow rate divided by nominal flow rate [1]

Outputs

Type	Name	Description
Real	eta	Efficiency [1]

Modelica definition

partial function baseEfficiency 
  "Base class for efficiency characteristics"
  extends Modelica.Icons.Function;
  input Real r_V(unit="1") "Volumetric flow rate divided by nominal flow rate";
  output Real eta(min=0, unit="1") "Efficiency";
end baseEfficiency;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.linearFlow

Linear flow characteristic

Information

Extends from baseFlow (Base class for fan or pump flow characteristics).

Inputs

Type	Name	Default	Description
VolumeFlowRate	V_flow		Volumetric flow rate [m3/s]
Real	r_N		Relative revolution, r_N=N/N_nominal [1]
VolumeFlowRate	V_flow_nominal[2]		Volume flow rate for two operating points (single fan or pump) [m3/s]
Pressure	dp_nominal[2]		Fan or pump total pressure for two operating points [Pa]

Outputs

Type	Name	Description
Pressure	dp	Fan or pump total pressure [Pa]

Modelica definition

function linearFlow "Linear flow characteristic"
  extends baseFlow;

  input Modelica.SIunits.VolumeFlowRate V_flow_nominal[2] 
    "Volume flow rate for two operating points (single fan or pump)";
  input Modelica.SIunits.Pressure dp_nominal[2](each min=0, each displayUnit="Pa") 
    "Fan or pump total pressure for two operating points";
  /* Linear system to determine the coefficients:
  dp_nominal[1] = c[1] + V_flow_nominal[1]*c[2];
  dp_nominal[2] = c[1] + V_flow_nominal[2]*c[2];
  */
protected 
  Real c[2] = Buildings.Fluid.Movers.BaseClasses.Characteristics.solve( [ones(2),V_flow_nominal],dp_nominal) 
    "Coefficients of linear total pressure curve";
algorithm 
  dp := r_N^2 * c[1] + r_N*V_flow*c[2];
end linearFlow;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.quadraticFlow

Quadratic flow characteristic

Information

Extends from baseFlow (Base class for fan or pump flow characteristics).

Inputs

Type	Name	Default	Description
VolumeFlowRate	V_flow		Volumetric flow rate [m3/s]
Real	r_N		Relative revolution, r_N=N/N_nominal [1]
VolumeFlowRate	V_flow_nominal[3]		Volume flow rate for three operating points (single fan or pump) [m3/s]
Pressure	dp_nominal[3]		Fan or pump total pressure for three operating points [Pa]

Outputs

Type	Name	Description
Pressure	dp	Fan or pump total pressure [Pa]

Modelica definition

function quadraticFlow "Quadratic flow characteristic"
  extends baseFlow;
  input Modelica.SIunits.VolumeFlowRate V_flow_nominal[3](each min=0) 
    "Volume flow rate for three operating points (single fan or pump)";
  input Modelica.SIunits.Pressure dp_nominal[3](each min=0, each displayUnit="Pa") 
    "Fan or pump total pressure for three operating points";
protected 
  Real V_flow_nominal2[3] = {V_flow_nominal[1]^2,V_flow_nominal[2]^2, V_flow_nominal[3]^2} 
    "Squared nominal flow rates";
  /* Linear system to determine the coefficients:
  dp_nominal[1] = c[1] + V_flow_nominal[1]*c[2] + V_flow_nominal[1]^2*c[3];
  dp_nominal[2] = c[1] + V_flow_nominal[2]*c[2] + V_flow_nominal[2]^2*c[3];
  dp_nominal[3] = c[1] + V_flow_nominal[3]*c[2] + V_flow_nominal[3]^2*c[3];
  */
  Real c[3] = Buildings.Fluid.Movers.BaseClasses.Characteristics.solve( [ones(3), V_flow_nominal, V_flow_nominal2],dp_nominal) 
    "Coefficients of quadratic total pressure curve";
algorithm 
  // Flow equation: dp  = c[1] + V_flow*c[2] + V_flow^2*c[3];
  dp := r_N^2*c[1] + r_N*V_flow*c[2] + V_flow^2*c[3];
end quadraticFlow;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.polynomialFlow

Polynomial flow characteristic

Information

Extends from baseFlow (Base class for fan or pump flow characteristics).

Inputs

Type	Name	Default	Description
VolumeFlowRate	V_flow		Volumetric flow rate [m3/s]
Real	r_N		Relative revolution, r_N=N/N_nominal [1]
VolumeFlowRate	V_flow_nominal[:]		Volume flow rate for N operating points (single fan or pump) [m3/s]
Pressure	dp_nominal[:]		Fan or pump total pressure for N operating points [Pa]

Outputs

Type	Name	Description
Pressure	dp	Fan or pump total pressure [Pa]

Modelica definition

function polynomialFlow "Polynomial flow characteristic"
  extends baseFlow;
  input Modelica.SIunits.VolumeFlowRate V_flow_nominal[:](each min=0) 
    "Volume flow rate for N operating points (single fan or pump)";
  input Modelica.SIunits.Pressure dp_nominal[:](each min=0, each displayUnit="Pa") 
    "Fan or pump total pressure for N operating points";
protected 
  Integer N = size(V_flow_nominal,1) "Number of nominal operating points";
  Real V_flow_nominal_pow[N,N] = {{V_flow_nominal[i]^(j-1) for j in 1:N} for i in 1:N} 
    "Rows: different operating points; columns: increasing powers";
  /* Linear system to determine the coefficients (example N=3):
  dp_nominal[1] = c[1] + V_flow_nominal[1]*c[2] + V_flow_nominal[1]^2*c[3];
  dp_nominal[2] = c[1] + V_flow_nominal[2]*c[2] + V_flow_nominal[2]^2*c[3];
  dp_nominal[3] = c[1] + V_flow_nominal[3]*c[2] + V_flow_nominal[3]^2*c[3];
  */
  Real c[N] = Buildings.Fluid.Movers.BaseClasses.Characteristics.solve( V_flow_nominal_pow,dp_nominal) 
    "Coefficients of polynomial total pressure curve";
algorithm 
  // Flow equation (example N=3): dp  = c[1] + V_flow*c[2] + V_flow^2*c[3];
  // Note: the implementation is numerically efficient only for low values of N
  dp := r_N^(N-1)*c[1] + sum(r_N^(N-i)*V_flow^(i-1)*c[i] for i in 2:N-1) + V_flow^(N-1)*c[N];
end polynomialFlow;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.linearPower

Linear power consumption characteristic

Information

Extends from basePower (Base class for fan or pump power consumption characteristics).

Inputs

Type	Name	Default	Description
VolumeFlowRate	V_flow		Volumetric flow rate [m3/s]
Real	r_N		Relative revolution, r_N=N/N_nominal [1]
VolumeFlowRate	V_flow_nominal[2]		Volume flow rate for two operating points (single fan or pump) [m3/s]
Power	P_nominal[2]		Power consumption for two operating points [W]

Outputs

Type	Name	Description
Power	consumption	Power consumption [W]

Modelica definition

function linearPower "Linear power consumption characteristic"
  extends basePower;
  input Modelica.SIunits.VolumeFlowRate V_flow_nominal[2] 
    "Volume flow rate for two operating points (single fan or pump)";
  input Modelica.SIunits.Power P_nominal[2] 
    "Power consumption for two operating points";
  /* Linear system to determine the coefficients:
  P_nominal[1] = c[1] + V_flow_nominal[1]*c[2];
  P_nominal[2] = c[1] + V_flow_nominal[2]*c[2];
  */
protected 
  Real c[2] = Buildings.Fluid.Movers.BaseClasses.Characteristics.solve( [ones(3),V_flow_nominal],P_nominal) 
    "Coefficients of linear power consumption curve";
algorithm 
  consumption := r_N^3*c[1] + r_N^2*V_flow*c[2];
end linearPower;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.quadraticPower

Quadratic power consumption characteristic

Information

Extends from basePower (Base class for fan or pump power consumption characteristics).

Inputs

Type	Name	Default	Description
VolumeFlowRate	V_flow		Volumetric flow rate [m3/s]
Real	r_N		Relative revolution, r_N=N/N_nominal [1]
VolumeFlowRate	V_flow_nominal[3]		Volume flow rate for three operating points (single fan or pump) [m3/s]
Power	P_nominal[3]		Power consumption for three operating points [W]

Outputs

Type	Name	Description
Power	consumption	Power consumption [W]

Modelica definition

function quadraticPower "Quadratic power consumption characteristic"
  extends basePower;
  input Modelica.SIunits.VolumeFlowRate V_flow_nominal[3] 
    "Volume flow rate for three operating points (single fan or pump)";
  input Modelica.SIunits.Power P_nominal[3] 
    "Power consumption for three operating points";
protected 
  Real V_flow_nominal2[3] = {V_flow_nominal[1]^2,V_flow_nominal[2]^2, V_flow_nominal[3]^2} 
    "Squared nominal flow rates";
  /* Linear system to determine the coefficients:
  P_nominal[1] = c[1] + V_flow_nominal[1]*c[2] + V_flow_nominal[1]^2*c[3];
  P_nominal[2] = c[1] + V_flow_nominal[2]*c[2] + V_flow_nominal[2]^2*c[3];
  P_nominal[3] = c[1] + V_flow_nominal[3]*c[2] + V_flow_nominal[3]^2*c[3];
  */
  Real c[3] = Buildings.Fluid.Movers.BaseClasses.Characteristics.solve( [ones(3),V_flow_nominal,V_flow_nominal2],P_nominal) 
    "Coefficients of quadratic power consumption curve";
algorithm 
  consumption := r_N^3*c[1] + r_N^2*V_flow*c[2] + r_N*V_flow^2*c[3];
end quadraticPower;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.polynomialPower

Polynomial power consumption characteristic

Information

Extends from basePower (Base class for fan or pump power consumption characteristics).

Inputs

Type	Name	Default	Description
VolumeFlowRate	V_flow		Volumetric flow rate [m3/s]
Real	r_N		Relative revolution, r_N=N/N_nominal [1]
VolumeFlowRate	V_flow_nominal[:]		Volume flow rate for N operating points (single fan or pump) [m3/s]
Power	P_nominal[:]		Power consumption for N operating points [W]

Outputs

Type	Name	Description
Power	consumption	Power consumption [W]

Modelica definition

function polynomialPower 
  "Polynomial power consumption characteristic"
  extends basePower;
  input Modelica.SIunits.VolumeFlowRate V_flow_nominal[:] 
    "Volume flow rate for N operating points (single fan or pump)";
  input Modelica.SIunits.Power P_nominal[:] 
    "Power consumption for N operating points";
protected 
  Integer N = size(V_flow_nominal,1) "Number of nominal operating points";
  Real V_flow_nominal_pow[N,N] = {{V_flow_nominal[i]^(j-1) for j in 1:N} for i in 1:N} 
    "Rows: different operating points; columns: increasing powers";
  /* Linear system to determine the coefficients (example N=3):
  P_nominal[1] = c[1] + V_flow_nominal[1]*c[2] + V_flow_nominal[1]^2*c[3];
  P_nominal[2] = c[1] + V_flow_nominal[2]*c[2] + V_flow_nominal[2]^2*c[3];
  P_nominal[3] = c[1] + V_flow_nominal[3]*c[2] + V_flow_nominal[3]^2*c[3];
  */
  Real c[N] = Buildings.Fluid.Movers.BaseClasses.Characteristics.solve( V_flow_nominal_pow,P_nominal) 
    "Coefficients of polynomial power consumption curve";
algorithm 
  // Efficiency equation (example N=3): W  = c[1] + V_flow*c[2] + V_flow^2*c[3];
  // Note: the implementation is numerically efficient only for low values of N
  consumption := r_N^N*c[1] + sum(r_N^(N-i+1)*V_flow^(i-1)*c[i] for i in 2:N);
end polynomialPower;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.constantEfficiency

Constant efficiency characteristic

Information

Extends from baseEfficiency (Base class for efficiency characteristics).

Inputs

Type	Name	Default	Description
Real	r_V		Volumetric flow rate divided by nominal flow rate [1]
Real	eta_nominal		Nominal efficiency [1]

Outputs

Type	Name	Description
Real	eta	Efficiency [1]

Modelica definition

function constantEfficiency "Constant efficiency characteristic"
   extends baseEfficiency;
   input Real eta_nominal(min=0, unit="1") "Nominal efficiency";
algorithm 
  eta := eta_nominal;
end constantEfficiency;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.linearEfficiency

Linear efficiency characteristic

Information

Extends from baseEfficiency (Base class for efficiency characteristics).

Inputs

Type	Name	Default	Description
Real	r_V		Volumetric flow rate divided by nominal flow rate [1]
Real	r_V_nominal[2]		Volumetric flow rate divided by nominal flow rate for two operating points (single fan or pump) [1]
Real	eta_nominal[2]		Nominal efficiency [1]

Outputs

Type	Name	Description
Real	eta	Efficiency [1]

Modelica definition

function linearEfficiency "Linear efficiency characteristic"
  extends baseEfficiency;
  input Real r_V_nominal[2](each unit="1") 
    "Volumetric flow rate divided by nominal flow rate for two operating points (single fan or pump)";
  input Real eta_nominal[2](each min=0, each unit="1") "Nominal efficiency";
  /* Linear system to determine the coefficients:
  eta_nominal[1] = c[1] + V_flow_nominal[1]*c[2];
  eta_nominal[2] = c[1] + V_flow_nominal[2]*c[2];
  */
protected 
  Real c[2] = Buildings.Fluid.Movers.BaseClasses.Characteristics.solve( [ones(2),r_V_nominal],eta_nominal) 
    "Coefficients of linear total efficiency curve";
algorithm 
  // Efficiency equation: eta = q*c[1] + c[2];
  eta := c[1] + r_V*c[2];
end linearEfficiency;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.quadraticEfficiency

Quadratic efficiency characteristic

Information

Extends from baseEfficiency (Base class for efficiency characteristics).

Inputs

Type	Name	Default	Description
Real	r_V		Volumetric flow rate divided by nominal flow rate [1]
Real	r_V_nominal[3]		Volumetric flow rate divided by nominal flow rate for three operating points (single fan or pump) [1]
Real	eta_nominal[3]		Nominal efficiency for three operating points [1]

Outputs

Type	Name	Description
Real	eta	Efficiency [1]

Modelica definition

function quadraticEfficiency "Quadratic efficiency characteristic"
  extends baseEfficiency;
  input Real r_V_nominal[3](each unit="1") 
    "Volumetric flow rate divided by nominal flow rate for three operating points (single fan or pump)";
  input Real eta_nominal[3](each min=0, each unit="1") 
    "Nominal efficiency for three operating points";
protected 
  Real r_V_nominal2[3] = {r_V_nominal[1]^2,r_V_nominal[2]^2, r_V_nominal[3]^2} 
    "Squared nominal flow rates";
  /* Linear system to determine the coefficients:
  eta_nominal[1] = c[1] + r_V_nominal[1]*c[2] + r_V_nominal[1]^2*c[3];
  eta_nominal[2] = c[1] + r_V_nominal[2]*c[2] + r_V_nominal[2]^2*c[3];
  eta_nominal[3] = c[1] + r_V_nominal[3]*c[2] + r_V_nominal[3]^2*c[3];
  */
  Real c[3] = Buildings.Fluid.Movers.BaseClasses.Characteristics.solve( [ones(3), r_V_nominal, r_V_nominal2],eta_nominal) 
    "Coefficients of quadratic efficiency curve";
algorithm 
  // Efficiency equation: eta  = c[1] + V_flow*c[2] + V_flow^2*c[3];
  eta := c[1] + r_V*c[2] + r_V^2*c[3];
end quadraticEfficiency;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.polynomialEfficiency

Polynomial efficiency characteristic

Information

Extends from baseEfficiency (Base class for efficiency characteristics).

Inputs

Type	Name	Default	Description
Real	r_V		Volumetric flow rate divided by nominal flow rate [1]
Real	r_V_nominal[:]		Volumetric flow rate divided by nominal flow rate for N operating points (single fan or pump) [1]
Real	eta_nominal[:]		Nominal efficiency for N operating points [1]

Outputs

Type	Name	Description
Real	eta	Efficiency [1]

Modelica definition

function polynomialEfficiency "Polynomial efficiency characteristic"
  extends baseEfficiency;
  input Real r_V_nominal[:](each unit="1") 
    "Volumetric flow rate divided by nominal flow rate for N operating points (single fan or pump)";
  input Real eta_nominal[:](each min=0, each unit="1") 
    "Nominal efficiency for N operating points";
protected 
  Integer N = size(r_V_nominal,1) "Number of nominal operating points";
  Real r_V_nominal_pow[N,N] = {{r_V_nominal[i]^(j-1) for j in 1:N} for i in 1:N} 
    "Rows: different operating points; columns: increasing powers";
  /* Linear system to determine the coefficients (example N=3):
  eta_nominal[1] = c[1] + r_V_nominal[1]*c[2] + r_V_nominal[1]^2*c[3];
  eta_nominal[2] = c[1] + r_V_nominal[2]*c[2] + r_V_nominal[2]^2*c[3];
  eta_nominal[3] = c[1] + r_V_nominal[3]*c[2] + r_V_nominal[3]^2*c[3];
  */
  Real c[N] = Buildings.Fluid.Movers.BaseClasses.Characteristics.solve( r_V_nominal_pow,eta_nominal) 
    "Coefficients of polynomial total pressure curve";
algorithm 
  // Efficiency equation (example N=3): eta  = c[1] + r_V*c[2] + r_V^2*c[3];
  // Note: the implementation is numerically efficient only for low values of N
  eta := c[1] + sum(r_V^(i-1)*c[i] for i in 2:N);
end polynomialEfficiency;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.solve

Wrapper for Modelica.Math.Matrices.solve

Information

Wrapper function for Modelica.Math.Matrices.solve. This is currently needed since Modelica.Math.Matrices.solve does not specify a derivative. The implementation is based on the code from Hans Olsson, Dynasim support request 10872.

Inputs

Type	Name	Default	Description
Real	A[:, size(A, 1)]
Real	x[size(A, 1)]

Outputs

Type	Name	Description
Real	b[size(A, 1)]

Modelica definition

function solve "Wrapper for Modelica.Math.Matrices.solve"
  annotation(derivative=Buildings.Fluid.Movers.BaseClasses.Characteristics.der_solve);
 input Real A[:,size(A,1)];
 input Real x[size(A,1)];
output Real b[size(A,1)];
algorithm 
 b:=Modelica.Math.Matrices.solve(A,x);

end solve;

---

Buildings.Fluid.Movers.BaseClasses.Characteristics.der_solve

Derivative for function solve

Inputs

Type	Name	Default	Description
Real	A[:, size(A, 1)]
Real	x[size(A, 1)]
Real	Ader[:, size(A, 1)]
Real	xder[size(A, 1)]

Outputs

Type	Name	Description
Real	b[size(A, 1)]

Modelica definition

function der_solve "Derivative for function solve"
  input Real A[:,size(A,1)];
  input Real x[size(A,1)];
  input Real Ader[:,size(A,1)];
  input Real xder[size(A,1)];
  output Real b[size(A,1)];
algorithm 
  b:=Modelica.Math.Matrices.solve(A,xder-Ader*Modelica.Math.Matrices.solve(A,x));
end der_solve;

---

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