_{1}

The sensitivity of power system stability (including transient and dynamic stabilities) to generator parameters (including parameters of generator model, excitation system and power system stabilizer) is analyzed in depth by simulations. From the tables and plots of the resultant simulated data, a number of useful rules are revealed. These rules can be directly applied to the engineering checking of generator parameters. Because the complex theoretical analyses are circumvented, the checking procedure is greatly simplified, remarkably promoting the working efficiency of electrical engineers on site.

Generators are the most important component of power system, and thus the level of power system stability is closely related to generator parameters [

The main contribution of this paper is based on the actual engineering experiences of the author. From plenty of simulation experiments, the sensitivity of power system stability (including transient stability and dynamic stability) to generator parameters is analyzed and illustrated in detail, and as a result some feasible and fast rules for testing and checking generator parameters are revealed and summarized, which can be directly adopted by the electrical engineers on site. And because the complex theoretical analyses are circumvented, the testing and checking procedure is greatly simplified so that the working efficiency of electrical engineers is greatly promoted.

The number and definitions of generator parameters are correlated with specific generator models. To ensure generality, the integral model of generator should be adopted, in which the stator consists of three-phase windings and the rotator consists of salient poles, excitation winding f, d-axis equivalent damping winding D and two q-axis equivalent damping windings g and Q. Based on the Park transform, the per-unit equations of the integral model of generator under dq0 coordinates are as follows (because the magnetic field produced by 0-axis current i_{0} in stator windings is 0 and has no effect on the electric characteristics of rotator [

{ υ d = − ψ q − R a i d υ q = ψ d − R a i q υ f = d ψ f / d t + R f i f 0 = d ψ D / d t + R D i D 0 = d ψ g / d t + R g i g 0 = d ψ Q / d t + R Q i Q { ψ d = − X d i d + X ad i f + X ad i D ψ f = − X ad i d + X f i f + X ad i D ψ D = − X ad i d + X ad i f + X D i D ψ q = − X q i q + X aq i g + X aq i Q ψ g = − X aq i q + X g i g + X aq i Q ψ Q = − X aq i q + X aq i g + X Q i Q (1)

where υ d , υ q and υ f are the voltages of d-axis, q-axis and excitation wingding f; i_{d}, i_{q}, i_{f}, i_{D}, i_{g} and i_{Q} are the currents of d-axis, q-axis, excitation wingding f, equivalent damping windings D, g and Q; R_{a}, R_{f}, R_{D}, R_{g} and R_{Q} are the resistances of one-phase stator winding, excitation winding f, equivalent damping windings D, g and Q; y_{d}, y_{q}, y_{f}, y_{D}, y_{g} and y_{Q} are the total magnetic flux linkages of d-axis and q-axis windings, excitation winding f, equivalent damping windings D, g and Q; X_{d}, X_{q}, X_{ad}, X_{aq}, X_{f}, X_{D}, X_{g} and X_{Q} are the synchronous reactances of d-axis and q-axis, the armature reaction reactances of d-axis and q-axis windings, the reactance of excitation winding f, the reactances of equivalent damping windings D, g and Q. And, in Equation (1) two assumptions are made: i) assume dy_{d}/dt ≈ 0 and dy_{q}/dt ≈ 0, that is, the electromagnetic transient process is not considered, or the aperiodic component of the stator current is considered in another way [_{d} and υ _{q} linearized.

Apparently, the total magnetic flux linkages y_{d}, y_{q}, y_{f}, y_{D}, y_{g} and y_{Q} in Equation (1) are inconvenient or even impossible to measure in practice, and therefore some measurable variables are introduced to represent these magnetic flux linkages indirectly:

{ E ′ d = − X aq ψ g / X g E ′ q = X ad ψ f / X f { E ″ d = − X aq ( X σg ψ Q + X σQ ψ g ) / ( X Q X g − X aq 2 ) E ″ q = X ad ( X σD ψ f + X σf ψ D ) / ( X D X f − X ad 2 ) (2)

where E ′ d , E ′ q and E ″ d , E ″ q are the transient and subtransient electromotive forces of d-axis and q-axis; X_{s}_{f}, X_{s}_{D}, X_{s}_{g} and X_{s}_{Q} are the leakage reactances of excitation winding f, equivalent damping windings D, g and Q.

Further, some measurable parameters are also introduced, not only simplifying the equations but also making the equations’ physical meanings clearer:

{ T ′ d 0 = X f / R f T ′ q 0 = X g / R g { T ″ d 0 = ( X D − X ad 2 / X f ) / R D T ″ q 0 = ( X Q − X aq 2 / X g ) / R Q (3)

where T ′ d 0 , T ′ q 0 and T ″ d 0 , T ″ q 0 are the open circuit transient and subtransient time constants of d-axis and q-axis.

By substituting Equations (2) and (3) into Equation (1), the 6^{th}-order practical model of generator can be derived:

{ { υ d = E ″ d + X ″ q i q − R a i d υ q = E ″ q − X ″ d i d − R a i q T ′ d 0 d E ′ q d t = X ad υ f R f − X d − X σa X ′ d − X σa E ′ q + X d − X ′ d X ′ d − X σa E ″ q − ( X d − X ′ d ) ( X ″ d − X σa ) X ′ d − X σa i d T ″ d 0 d E ″ q d t = X ″ d − X σa X ′ d − X σa T ″ d 0 d E ′ q d t − E ″ q + E ′ q + ( X ′ d − X ″ d ) i d T ′ q0 d E ′ d d t = − X q − X σa X ′ q − X σa E ′ d + X q − X ′ q X ′ q − X σa E ″ d + ( X q − X ′ q ) ( X ″ q − X σa ) X ′ q − X σa i q T ″ q0 d E ″ d d t = X ″ q − X σa X ′ q − X σa T ″ q0 d E ′ d d t − E ″ d + E ′ d + ( X ′ q − X ″ q ) i q d δ d t = ω − 1 (4)

where X_{s}_{a}, X ′ d , X ′ q and X ″ d , X ″ d are the leakage reactance of stator winding, the transient and subtransient reactances of d-axis and q-axis. And the 6 equations are the voltage equations of stator, excitation winding f, equivalent damping windings D, g and Q, and the motion equation of stator, successively. From Equation (4), the specific position of each generator parameter in the formula is determined clearly.

By reducing Equation (4) to different extent, i.e., neglecting a certain number of windings or introducing new assumptions, the 5^{th}-order, 4^{th}-order, 3^{rd}-order and 2^{nd}-order models of generator can be obtained [

1) Rules for the 6^{th}-order model (in this model d-axis, q-axis windings, excitation winding f and equivalent damping windings D, g and Q are all considered, and it is the detailed model of solid steam turbine or non-salient pole machine): T ′ q0 > 0 , X q ≠ X ′ q .

2) Rules for the 5^{th}-order model (in this model equivalent damping winding g is neglected, and it is the detailed model of hydraulic turbine or salient pole machine): T ′ q0 = 0 , X q ≠ X ′ q .

3) Rules for the 4^{th}-order model (in this model only d-axis, q-axis windings, excitation winding f and equivalent damping winding g are considered, and it is suitable for describing the solid steam turbine): T ′ q0 > 0 , X q ≠ X ′ q .

4) Rules for the 3^{rd}-order model (in this model only d-axis, q-axis windings and excitation winding f are considered, and it is suitable for describing the salient pole machine when high computational accuracy is not required): T ′ q0 = 0 , X q = X ′ q .

5) Rules for the 2^{nd}-order model (in this model it is assumed that the excitation system is so strong that it can maintain the constancy of E ′ d and E ′ q ): T ′ d 0 = a very big value.

6) Rules for both the salient and non-salient pole machines: X q ≠ X ′ d .

The rules above are merely the qualitative rules, and a number of quantitative testing and checking rules (variation ranges) [

Provided that the generator parameters are prominently deviating from the aforementioned 6 requirements, the above 2 rules and the reference ranges of

The testing and checking rules of generator parameters presented in Section 3 are necessary conditions but not sufficient conditions to guarantee power system

Parameter name (unit) | Notation | Steam turbine | Hydraulic turbine |
---|---|---|---|

Synchronous reactances (p.u.) | X_{d} | 1.0 - 2.3 | 0.6 - 1.5 |

X_{q} | 1.0 - 2.3 | 0.4 - 1.0 | |

Transient reactances (p.u.) | X ′ d | 0.15 - 0.4 | 0.2 - 0.5 |

X ′ q | 0.2 - 1.0 | 0.2 - 1.0 | |

Subtransient reactances (p.u.) | X ″ d | 0.1 - 0.25 | 0.15 - 0.35 |

X ″ q | 0.1 - 0.25 | 0.2 - 0.45 | |

Open circuit transient time constants (s) | T ′ d0 | 3.0 - 10.0 | 1.5 - 9.0 |

T ′ q0 | 0.5 - 2.0 | 0 - 2.0 | |

Open circuit subtransient time constants (s) | T ″ d0 | 0.02 - 0.05 | 0.01 - 0.05 |

T ″ q0 | 0.02 - 0.07 | 0.01 - 0.09 | |

Stator leakage reactance (p.u.) | X_{s}_{a} | 0.05 - 0.2 | 0.05 - 0.2 |

Stator resistor (p.u.) | R_{a} | 0.0015 - 0.005 | 0.0015 - 0.005 |

Inertia time constant (s) | T_{J} | 4.0 - 8.0 | 8.0 - 16.0 |

stability. Whether power system can maintain stable or not depends also on generator parameters’ combinations. This section is aimed at analyzing and illustrating the sensitivity of power system stability (including transient stability and dynamic stability) to generator parameters’ combinations by plenty of simulation experiments. To make it possible for readers to reproduce the simulation results, the IEEE 9-node test system is selected as the simulation model. And the simulation experiments are carried out on one of the most famous simulation software platforms of power system, the Chinese edition BPA, i.e. PSD-BPA (Power System Department―Bonneville Power Administration) [

The geographically interconnected diagram of the IEEE 9-node test system is shown in _{a} ≈ 0, R_{a} is omitted from

By comparing the generator parameters in

X_{d} | X_{q} | X ′ d | X ′ q | X ″ d | X ″ q | |
---|---|---|---|---|---|---|

GEN1 | 0.1460 | 0.0969 | 0.0608 | 0.0969 | 0.0400 | 0.0600 |

GEN2 | 0.8958 | 0.8645 | 0.1189 | 0.1969 | 0.0890 | 0.0890 |

GEN3 | 1.3130 | 1.2580 | 0.1813 | 0.2500 | 0.1070 | 0.1070 |

T ′ d0 | T ′ d0 | T ″ d0 | T ″ q0 | X_{s}_{a} | T_{J} | |

GEN1 | 8.9600 | 0 | 0.0400 | 0.0600 | 0.0336 | 47.280 |

GEN2 | 6.0000 | 0.5400 | 0.0330 | 0.0780 | 0.0521 | 12.800 |

GEN3 | 5.8900 | 0.6000 | 0.0330 | 0.0700 | 0.0742 | 6.0200 |

not be obeyed inflexibly, and generator parameters’ combinations should also be taken into consideration.

From a good many simulation experiments, the author finds that the transient stability of power system is very sensitive to the values of X ″ d / X ′ d and X ″ q / X ′ q . If one of these two values is greater than 0.95, under large-disturbance the power angle curve of generator tends to oscillate greatly and damp slowly, or even diverges, implying generator is out of transient stability. Simulation results in

BUS1-STATION B: at 0 s, a three-phase short-circuit fault occurs on the side of STATION B; at 0.2 s, the breakers on both sides trip to clear the fault but do not reclose. From the comparison of the power angle curves in

The large-disturbance set in the simulation of

The common steps to analyze the dynamic stability of power system are as follows.

1) Use the small-disturbance analysis method, i.e. the frequency-domain method, to decompose the oscillation modes, and then calculate the real part, imaginary part, frequency and damping ratio of each oscillation mode, together with the electromechanical circuit correlation ratio, the modulus and phase angle of the right eigenvector, and the participation factors of the generators participating in the oscillation.

2) Use Prony method, a famous time-domain method, to analyze the active powers of some important interconnection transmission lines under large-disturbance and decompose them into a number of oscillation modes as well.

3) Try to find out the oscillation modes under large-disturbance, which are consistent with those found by small-disturbance analysis. If such oscillation modes are found, it can be concluded that the analytic results in frequency domain and time domain are consistent with each other, and that the dynamic stability analysis above is valid.

According to the foregoing steps, firstly, apply the small-disturbance analysis to the IEEE 9-node test system. From the small-disturbance analysis, 6 oscillation modes are obtained, wherein only 1 oscillation mode has an electromechanical circuit correlation ratio that is greater than 1.0, meaning that it is the dominant oscillation mode (DOM). Due to this, for brevity, the tables and figures in this subsection show only the details of this DOM. And in Tables 3-7 and Figures 4-8, the sensitivities of the frequency and damping ratio of the DOM to GEN3’s parameters T ′ d0 , T ′ q0 , T ″ d0 , T ″ q0 and T_{J} are illustrated respectively, where the variation ranges of GEN3’s parameters are conform to

T ′ d0 (s) | 3.00 | 3.70 | 4.40 | 5.10 | 5.80 | 6.50 |
---|---|---|---|---|---|---|

Frequency (Hz) | 1.3364 | 1.3248 | 1.3159 | 1.3091 | 1.3038 | 1.2994 |

Damping ratio (%) | 7.17 | 6.86 | 6.53 | 6.21 | 5.92 | 5.67 |

T ′ d0 (s) | 7.20 | 7.90 | 8.60 | 9.30 | 10.0 | |

Frequency (Hz) | 1.2959 | 1.2929 | 1.2904 | 1.2882 | 1.2862 | |

Damping ratio (%) | 5.44 | 5.24 | 5.06 | 4.91 | 4.76 |

T ′ q0 (s) | 0.50 | 0.65 | 0.80 | 0.95 | 1.10 | 1.25 |
---|---|---|---|---|---|---|

Frequency (Hz) | 1.3028 | 1.3033 | 1.3039 | 1.3044 | 1.3049 | 1.3055 |

Damping ratio (%) | 5.82 | 5.92 | 5.99 | 6.04 | 6.08 | 6.12 |

T ′ q0 (s) | 1.40 | 1.55 | 1.70 | 1.85 | 2.00 | |

Frequency (Hz) | 1.3057 | 1.3061 | 1.3063 | 1.3067 | 1.3069 | |

Damping ratio (%) | 6.13 | 6.16 | 6.17 | 6.18 | 6.19 |

T ″ d0 (s) | 0.020 | 0.023 | 0.026 | 0.029 | 0.032 | 0.035 |
---|---|---|---|---|---|---|

Frequency (Hz) | 1.3023 | 1.3025 | 1.3028 | 1.3030 | 1.3032 | 1.3032 |

Damping ratio (%) | 6.30 | 6.20 | 6.10 | 6.01 | 5.89 | 5.83 |

T ″ d0 (s) | 0.038 | 0.041 | 0.044 | 0.047 | 0.050 | |

Frequency (Hz) | 1.3033 | 1.3034 | 1.3034 | 1.3034 | 1.3033 | |

Damping ratio (%) | 5.74 | 5.65 | 5.57 | 5.49 | 5.41 |

T ″ q0 (s) | 0.020 | 0.025 | 0.030 | 0.035 | 0.040 | 0.045 |
---|---|---|---|---|---|---|

Frequency (Hz) | 1.3088 | 1.3080 | 1.3072 | 1.3066 | 1.3060 | 1.3054 |

Damping ratio (%) | 5.53 | 5.57 | 5.60 | 5.64 | 5.68 | 5.71 |

T ″ q0 (s) | 0.050 | 0.055 | 0.060 | 0.065 | 0.070 | |

Frequency (Hz) | 1.3049 | 1.3044 | 1.3039 | 1.3035 | 1.3032 | |

Damping ratio (%) | 5.75 | 5.79 | 5.82 | 5.85 | 5.89 |

damping ratio has a small tendency of increasing. _{J} is smaller than a specific value, e.g. 6.5s as shown in _{J}.

T_{J} (s) | 4.00 | 4.40 | 4.80 | 5.20 | 5.60 | 6.00 |
---|---|---|---|---|---|---|

Frequency (Hz) | 1.3001 | 1.3017 | 1.3037 | 1.3062 | 1.3089 | 1.3118 |

Damping ratio (%) | 5.41 | 5.70 | 5.94 | 6.15 | 6.32 | 6.45 |

T_{J} (s) | 6.40 | 6.80 | 7.20 | 7.60 | 8.00 | |

Frequency (Hz) | 1.3147 | 1.3175 | 1.3201 | 1.3226 | 1.3248 | |

Damping ratio (%) | 6.53 | 6.59 | 6.61 | 6.61 | 6.60 |

Secondly, apply the large-disturbance analysis to the IEEE 9-node test system to testify the simulation results derived from the preceding small-disturbance analysis. The large disturbance set in the simulation here is the same three-phase permanent fault on 220 kV transmission line BUS1-STATION B as the one in Subsection 4.2. And the resultant active power of the 220 kV transmission line BUS2-STATION A is analyzed by Prony method. Likewise, in Tables 8-12 and Figures 9-13, the sensitivities of the frequency and damping ratio of the DOM to GEN3’s parameters T ′ d0 , T ′ q0 , T ″ d0 , T ″ q0 and T_{J} are illustrated respectively.

_{J} is smaller than a specific value, e.g. 6.5 s as shown in _{J}, while the damping ratio is first increasing and then (at about 4.7 s) decreasing.

Now, by successively comparing the simulation results obtained from the time-domain method under large disturbance with those obtained from the frequency-domain method under small disturbance, we can see that the DOM’s frequency changes with generator parameters in both the time-domain analysis

T ′ d0 (s) | 3.00 | 3.70 | 4.40 | 5.10 | 5.80 | 6.50 |
---|---|---|---|---|---|---|

Frequency (Hz) | 1.366 | 1.341 | 1.309 | 1.241 | 1.245 | 1.152 |

Damping ratio (%) | 14.100 | 16.299 | 18.870 | 20.834 | 28.129 | 17.284 |

T ′ d0 (s) | 7.20 | 7.90 | 8.60 | 9.30 | 10.0 | |

Frequency (Hz) | 1.142 | 1.137 | 1.133 | 1.130 | 1.127 | |

Damping ratio (%) | 15.039 | 13.519 | 12.315 | 11.375 | 10.545 |

T ′ q0 (s) | 0.50 | 0.65 | 0.80 | 0.95 | 1.10 | 1.25 |
---|---|---|---|---|---|---|

Frequency (Hz) | 1.162 | 1.153 | 1.160 | 1.212 | 1.137 | 1.174 |

Damping ratio (%) | 19.826 | 20.667 | 21.922 | 20.643 | 23.690 | 20.886 |

T ′ q0 (s) | 1.40 | 1.55 | 1.70 | 1.85 | 2.00 | |

Frequency (Hz) | 1.137 | 1.188 | 1.187 | 1.200 | 1.124 | |

Damping ratio (%) | 23.974 | 21.453 | 21.711 | 20.818 | 24.803 |

T ″ d0 (s) | 0.020 | 0.023 | 0.026 | 0.029 | 0.032 | 0.035 |
---|---|---|---|---|---|---|

Frequency (Hz) | 1.262 | 1.203 | 1.251 | 1.166 | 1.219 | 1.174 |

Damping ratio (%) | 25.667 | 24.390 | 26.483 | 22.538 | 28.185 | 30.647 |

T ″ d0 (s) | 0.038 | 0.041 | 0.044 | 0.047 | 0.050 | |

Frequency (Hz) | 1.194 | 1.184 | 1.186 | 1.189 | 1.192 | |

Damping ratio (%) | 31.080 | 18.083 | 17.250 | 16.728 | 16.095 |

T ″ q0 (s) | 0.020 | 0.025 | 0.030 | 0.035 | 0.040 | 0.045 |
---|---|---|---|---|---|---|

Frequency (Hz) | 1.198 | 1.195 | 1.190 | 1.191 | 1.182 | 1.173 |

Damping ratio (%) | 17.260 | 17.330 | 17.199 | 17.756 | 18.688 | 18.955 |

T ″ q0 (s) | 0.050 | 0.055 | 0.060 | 0.065 | 0.070 | |

Frequency (Hz) | 1.180 | 1.175 | 1.172 | 1.166 | 1.186 | |

Damping ratio (%) | 17.896 | 19.287 | 20.799 | 21.297 | 29.204 |

and frequency-domain analysis are consistent with each other, while the DOM’s damping ratio changes with generator parameters, except T ′ q0 and T ″ q0 , are different from each other. It is because the frequency of an oscillation mode is determined by the inherent structural characteristic of power system, and thus is irrelevant to the operation mode and disturbance type of power system. And it is

T_{J} (s) | 4.00 | 4.40 | 4.80 | 5.20 | 5.60 | 6.00 |
---|---|---|---|---|---|---|

Frequency (Hz) | 1.144 | 1.149 | 1.153 | 1.205 | 1.249 | 1.268 |

Damping ratio (%) | 14.950 | 17.870 | 21.542 | 21.070 | 19.780 | 18.923 |

T_{J} (s) | 6.40 | 6.80 | 7.20 | 7.60 | 8.00 | |

Frequency (Hz) | 1.285 | 1.295 | 1.302 | 1.309 | 1.310 | |

Damping ratio (%) | 17.844 | 17.029 | 16.399 | 15.782 | 15.445 |

like the natural vibration frequency of a mechanical system. However, the damping ratio is not determined by the inherent structural characteristic of power system, and therefore it is sensitive to the operation mode and disturbance types of power system.

At the end of this section, two perspectives should be pointed out.

1) The non-dominant oscillation modes’ frequency and damping ratio changes with generator parameters are similar to those of the DOM’s, and therefore the conclusions derived from the DOM are applicable to the non-dominant oscillation modes.

2) If the damping ratio of certain oscillation mode is used to test and check generator parameters, the results obtained under small disturbance and large disturbance should be analyzed separately.

Except generator parameters per se, the adjustment of the parameters of excitation systems and PSS also plays an important role in ensuring the stability of generators and power system, and therefore the parameters of excitation systems and PSS are always treated as a requisite component of generator parameters. For this, this section proposes the engineering methods for testing and checking the parameters of excitation systems and PSS parameters.

The engineering method for testing and checking excitation systems parameters includes 4 steps.

1) Stop the operation of the PSS of the tested generator.

2) Isolate the tested generator from the electric network.

3) Adjust the reference voltage of excitation system according to a specific function, e.g. step function or ramp function.

4) Investigate whether the output voltage of generator is able to track the reference voltage effectively, and here the “effective track” means that the rising edge is steep, the overshoot is small and the steady area has no great oscillations.

It should be pointed out that a practical and effective way to finish step 4) is to compare the output voltage curve of the tested generator with that of a reference generator which has the correct parameters of both generator and excitation system. Here, the output voltage curve of the reference generator is named as classic curve. If the differences of the two curves are fairly small, it then can be inferred that the excitation system parameters are appropriate from the perspective of application; otherwise, it can be concluded that the excitation system parameters are inappropriate or ineffective, and should be adjusted again or measured directly from field test.

of GEN3 has good robustness. It should be noted that excitation system parameters depend mainly on the dynamic amplification coefficient of its automatic voltage regulator (AVR) [

The engineering method for testing and checking PSS parameters also includes 4 steps.

1) Set up the “double machines and double lines” simulation system as shown in

2) Set a three-phase permanent fault on transformer’s high-voltage side bus: at 0 s, a three-phase short-circuit fault occurs; at 0.1 s, the breakers on both sides of the transmission lines trip to clear the fault and do not reclose.

3) Switch on and off the PSS of GEN3, respectively.

4) Compare the damping speeds of the oscillations of GEN3’s output power under the two conditions above. If the damping speed of the oscillation of the output power is much faster when PSS is switched on than that when PSS is switched off, it can be concluded that PSS parameters are appropriate; otherwise, PSS parameters should be readjusted.

This paper analyzes the sensitivity of power system stability to generator parameters, including the parameters of generator, excitation system and PSS from plenty of simulation experiments. Because the simulation processes are closely related to the engineering practice and do not involve any complex theoretical analysis, the summarized rules and conclusions are evident and practical, and thus can be directly referenced or applied by electrical engineers. Based on these rules and conclusions, some feasible methods are proposed for testing and checking generator parameters quickly, which may greatly promote the working efficiencies of electrical engineers. Although the simulation examples used in this paper is very simple, the resultant conclusions are of generality and can be easily testified by readers in their researching and working activities.

This research is supported by the Science and Technology Research Project of Chongqing Educational Committee (KJ1603605) and the Natural Science Fund Project of Yongchuan District Science and Technology Committee (Ycstc, 2016nc3001).

The author declares no conflicts of interest regarding the publication of this paper.

Sun, X.M. (2019) Analysis on Sensitivity of Power System Stability to Generator Parameters. Journal of Power and Energy Engineering, 7, 165-182. https://doi.org/10.4236/jpee.2019.71009