An open-source Simulink-based program for simulating power systems integrated with renewable energy sources

Abstract

This paper presents an open-source Simulink-based program developed for simulating power systems integrated with renewable energy sources (RESs). The generic model of a photovoltaic, wind turbine, and battery energy storage is used for the RES. The program can be used for educational and research studies. It comes with several important subjects in power systems including power system modeling and integration, linearization, modal analysis, participation factor analysis, controller selection using residue analysis, and frequency response analysis. IEEE 68-bus dynamic test system is used to verify the performance of the program. The results show the efficiency and speed of the program to simulate a large-scale modern power system.

Appendices

Appendix 1: Abbreviations

$R_{\text{s}}$	Stator resistance in pu
$X_{d}$	d-axis reactance in pu
$X_{d}^{ '}$	Transient d-axis reactance in pu
$X_{d}^{\prime \prime }$	Sub-transient d-axis reactance in pu
$X_{q}$	q-axis reactance in pu
$X_{q}^{ '}$	Transient q-axis reactance in pu
$X_{q}^{\prime \prime }$	Sub-transient q-axis reactance in pu
$H$	Shaft inertia constant in s
$w_{\text{s}}$	Generator synchronous speed in rad per second
$T_{do}^{'}$	d-axis time constant associated with $E_{q}^{ '}$ in second
$T_{do}^{''}$	d-axis time constant associated with $\varPsi_{1d}$ in second
$T_{qo}^{'}$	q-axis time constant associated with $E_{d}^{ '}$ in second
$T_{qo}^{''}$	q-axis time constant associated with $\varPsi_{2q}$ in second
$T_{\text{A}}$	Amplifier time constant in s
$T_{\text{CH}}$	Incremental steam chest time constant in s
$T_{\text{SV}}$	Steam valve time constant in s
$K_{\text{A}}$	Amplifier gain
$K_{\text{E}}$	Separate or self-excited constant
$E_{q}^{ '}$	q-axis transient internal voltages in pu
$E_{d}^{ '}$	d-axis transient internal voltages in pu
$E$	Internal voltage in pu
$\varPsi_{1d}$	Damper winding 1d flux linkages in pu
$\varPsi_{2q}$	Damper winding 2q flux linkages in pu
$\delta$	Rotor angle in rad
$w$	Angular speed of generator in rad per second
$\bar{V}_{i}$	Complex voltage phasor
$V$	Magnitude of bus voltage in pu
$\theta$	Angle of bus voltage in rad
$\bar{I}_{Gi}$	Generator complex current phasor
$I_{Gi}$	Generator current magnitude in pu
$\gamma_{i}$	Generator current angle in rad
$I_{d}$	d-axis current in pu
$I_{q}$	q-axis current in pu
$\alpha_{ik}$	Angle of admittance $Y_{ik}$ in rad
$E_{fd}$	Field voltage in pu
$V_{R}$	Exciter input in pu
$R_{\text{F}}$	Rate feedback in pu
$T_{\text{M}}$	Mechanical input torque in pu
$P_{\text{SV}}$	Steam valve position in pu
$P_{\text{C}}$	Control power input in pu
$R_{\text{D}}$	Speed regulation quantity in Hz/pu
$V_{\text{ref}}$	Reference voltage input in pu
$S_{\text{E}}$	Saturation function
$T_{\text{FW}}$	Frictional windage torques

Appendix 2: Dynamic equations of the system

• 1. Synchronous generators

  $$ T_{doi}^{ '} \frac{{{\text{d}}E_{qi}^{ '} }}{{{\text{d}}t}} = - E_{qi}^{ '} - \left( {X_{di} - X_{di}^{ '} } \right)\left[ {I_{di} - \frac{{\left( {X_{di}^{ '} - X_{di}^{\prime \prime } } \right)}}{{\left( {X_{di}^{ '} - X_{ls} } \right)^{2} }}\left( {\varPsi_{1di} + \left( {X_{di}^{ '} - X_{ls} } \right)I_{di} - E_{qi}^{ '} } \right)} \right] + E_{fd} $$

  (10)
  $$ T_{doi}^{''} \frac{{{\text{d}}\varPsi_{1di} }}{{{\text{d}}t}} = - \varPsi_{1di} + E_{qi}^{'} - \left( {X_{di}^{'} - X_{ls} } \right)I_{di} $$

  (11)
  $$ T_{qoi}^{ '} \frac{{{\text{d}}E_{di}^{ '} }}{{{\text{d}}t}} = - E_{di}^{ '} + \left( {X_{qi} - X_{qi}^{ '} } \right)\left[ {I_{qi} - \frac{{\left( {X_{qi}^{ '} - X_{qi}^{\prime \prime } } \right)}}{{\left( {X_{qi}^{ '} - X_{ls} } \right)^{2} }}\left( {\varPsi_{2qi} + \left( {X_{qi}^{ '} - X_{ls} } \right)I_{qi} + E_{di}^{ '} } \right)} \right] $$

  (12)
  $$ T_{qoi}^{\prime \prime } \frac{{{\text{d}}\varPsi_{2qi} }}{{{\text{d}}t}} = - \varPsi_{2qi} - E_{di}^{ '} - \left( {X_{qi}^{ '} - X_{ls} } \right)I_{qi} $$

  (13)
  $$ \frac{{{\text{d}}\delta_{i} }}{{{\text{d}}t}} = w_{i} - w_{s} $$

  (14)
  $$ \begin{aligned} \frac{{2H_{i} }}{{w_{s} }}\frac{{{\text{d}}w_{i} }}{{{\text{d}}t}} & = T_{Mi} - \frac{{X_{di}^{''} - X_{ls} )}}{{\left( {X_{di}^{'} - X_{ls} } \right)}}E_{qi}^{'} I_{qi} - \frac{{\left( {X_{di}^{'} - X_{di}^{''} } \right)}}{{\left( {X_{di}^{'} - X_{ls} } \right)}}\varPsi_{1di} I_{qi} \\ & \quad - \,\frac{{\left( {X_{qi}^{''} - X_{ls} } \right)}}{{\left( {X_{qi}^{'} - X_{ls} } \right)}}E_{di}^{'} I_{di} + \frac{{\left( {X_{qi}^{'} - X_{qi}^{''} } \right)}}{{\left( {X_{qi}^{'} - X_{ls} } \right)}}\varPsi_{2qi} I_{di} \\ & \quad - \,\left( {X_{qi}^{''} - X_{di}^{''} } \right)I_{di} I_{qi} - T_{FW} \\ \end{aligned} $$

  (15)

• 2. Excitation systems (IEEE type I)

  $$ T_{Ei} \frac{{{\text{d}}E_{fdi} }}{{{\text{d}}t}} = - \left( {K_{Ei} + S_{Ei} \left( {E_{fdi} } \right)} \right)E_{fdi} + V_{Ri} $$

  (16)
  $$ T_{Fi} \frac{{{\text{d}}R_{fi} }}{{{\text{d}}t}} = - R_{fi} + \frac{{K_{fi} }}{{T_{fi} }}E_{fdi} $$

  (17)
  $$ \begin{aligned} T_{Ai} \frac{{{\text{d}}V_{Ri} }}{{{\text{d}}t}} & = - V_{Ri} + K_{Ai} R_{fi} \\ & \quad - \,\frac{{K_{Ai} K_{fi} }}{{T_{fi} }}E_{fdi} + K_{Ai} \left( {V_{{{\text{ref}}i}} - V_{i} } \right) \\ \end{aligned} $$

  (18)

• 3. Turbine systems

  $$ T_{{{\text{CH}}i}} \frac{{{\text{d}}T_{{{\text{M}}i}} }}{{{\text{d}}t}} = - T_{{{\text{M}}i}} + P_{{{\text{SV}}i}} $$

  (19)
  $$ T_{{{\text{SV}}i}} \frac{{{\text{d}}P_{{{\text{SV}}i}} }}{{{\text{d}}t}} = - P_{{{\text{SV}}i}} + P_{Ci} - \frac{1}{{R_{Di} }}\left( {\frac{{w_{i} }}{{w_{s} }} - 1} \right) $$

  (20)