/* ipDFT PMU hook.
*
* Author: Andres Acosta <andres.acosta@eonerc.rwth-aachen.de>
* SPDX-FileCopyrightText: 2014-2023 Institute for Automation of Complex Power Systems, RWTH Aachen University
* SPDX-License-Identifier: Apache-2.0
*/
#include <villas/hooks/pmu.hpp>
namespace villas {
namespace node {
class TruncatedIpDftPmuHook : public PmuHook {
protected:
std::complex<double> omega;
std::vector<std::vector<double>> twf_dft_r;
std::vector<std::vector<double>> twf_dft_i;
unsigned P;
unsigned startBin;
unsigned frequencyCount; // Number of requency bins that are calculated
double estimationRange; // The range around nominalFreq used for estimation
struct Complex {
double r;
double i;
double mag;
double ph;
double f;
};
struct PhasorReIm {
double r;
double i;
};
std::vector<Complex> Xk;
public:
TruncatedIpDftPmuHook(Path *p, Node *n, int fl, int prio, bool en = true)
: PmuHook(p, n, fl, prio, en), P(1), frequencyCount(0), estimationRange(0)
{}
PhasorReIm hann_frt(double k, unsigned M) {
PhasorReIm val;
double m = M_PI / M;
double a = 0.5 * sin(M_PI * k) / sin(k * M);
double b = 0.25 * sin(M_PI * (k+1)) / sin((k+1) * m);
double c = 0.25 * sin(M_PI * (k-1)) / sin((k-1) * m);
val.r = cos(k*(M-1)*m) * a - cos((k+1)*(M-1)*m) * b - cos((k-1)*(M-1)*m) * c;
val.i = -sin(k*(M-1)*m) * a + sin((k+1)*(M-1)*m) * b + sin((k-1)*(M-1)*m) * c;
return val;
}
void prepare() {
PmuHook::prepare();
// This is assuming that the window size (in number of samples) covers a period of the signal
// const double frequencyResolution = nominalFreq;
// Number of samples per frame consider minimum Fres<f0/2. Samples per reported phasor
// windowSize = sampleRate / frequencyResolution;
// Time window per frame (ms)
// const double Tw = 1000 / phasorRate;
// Number of frequency bins given the frequency resolution: Fres=Nr=Fs/Nc
if (phasorRate < 5) {
frequencyCount = 16;
} else {
frequencyCount = (nominalFreq / phasorRate) + 2;
}
if (frequencyCount%2 == 1) {
frequencyCount = frequencyCount + 1;
}
// Initialize matrix of dft coeffients
startBin = (unsigned)floor(nominalFreq/phasorRate - frequencyCount/2);
// unsigned endBin = startBin + frequencyCount;
twf_dft_r.clear();
twf_dft_i.clear();
// twf_dft_r.reserve(windowSize*frequencyCount);
// twf_dft_i.reserve(windowSize*frequencyCount);
for (unsigned k = 0; k < frequencyCount; k++) {
twf_dft_r.emplace_back(windowSize, 0.0);
twf_dft_i.emplace_back(windowSize, 0.0);
}
const double dw = 2* M_PI / frequencyCount;
// twiddle factor for truncated DFT
for (unsigned k = 0; k < frequencyCount; k++) {
for (unsigned n = 0; n < windowSize; n++) {
twf_dft_r[k][n] = cos(n*(k+startBin+1)*dw);
twf_dft_i[k][n] = sin(n*(k+startBin+1)*dw);
}
Xk.push_back({0., 0., 0., 0., 0.});
}
}
void parse(json_t *json) {
PmuHook::parse(json);
int ret;
json_error_t err;
assert(state != State::STARTED);
Hook::parse(json);
ret = json_unpack_ex(json, &err, 0, "{ s?: F}", "estimation_range",
&estimationRange);
if (ret)
throw ConfigError(json, err, "node-config-hook-ip-dft-pmu");
if (estimationRange <= 0)
throw ConfigError(
json, "node-config-hook-ip-dft-pmu-estimation_range",
"Estimation range cannot be less or equal than 0 tried to set {}",
estimationRange);
}
PmuHook::Phasor estimatePhasor(dsp::CosineWindow<double> *window,
PmuHook::Phasor lastPhasor) {
PmuHook::Phasor estimatedPhasor = {0};
const double B = 0.5*frequencyCount; // Integration of wh over the whole window
const double b = 1/B;
int km = 0;
double dfold = 0.0; // last df/dt of frequency
double df = 0.0; // df/dt of frequency
double d2fold = 0.0; // last d2f/dt2 of frequency
double d2f = 0.0; // d2f/dt2 of frequency
double rocof = 0.0; // ROCOF
double fold = 0.0; // last frequency value
double f = 0.0; // current frequency value
double state_rocof = false; // TRUE for Dynamic, False for Static State
for (unsigned n = 0; n < windowSize; n++) {
for (unsigned k = 0; k < frequencyCount; k++) {
// Real part of X[k]
Xk[k].r += (*window).val(n) * twf_dft_r[k][n];
// Imaginary part of X[k]
Xk[k].i -= (*window).val(n) * twf_dft_i[k][n];
}
}
for (unsigned k = 0; k < frequencyCount; k++) {
Xk[k].r *= b;
Xk[k].i *= b;
Xk[k].mag = pow(Xk[k].r*Xk[k].r + Xk[k].i*Xk[k].i, 0.5);
if (Xk[k].mag > Xk[km].mag) {
km = k;
}
}
std::vector<Complex> wXk = Xk;
// Windowing in Frequency Domain
for (unsigned k = 1; k < frequencyCount-1; k++) {
wXk[k].r = -0.25*Xk[k-1].r + 0.50*Xk[k].r - 0.25*Xk[k+1].r;
wXk[k].i = -0.25*Xk[k-1].i + 0.50*Xk[k].i - 0.25*Xk[k+1].i;
wXk[k].mag = pow(wXk[k].r*wXk[k].r + wXk[k].i*wXk[k].i, 0.5);
}
Xk = wXk;
int epsil = (Xk[km+1].mag > Xk[km-1].mag) ? 1 : -1;
double alpha = std::abs(Xk[km].mag / Xk[km+epsil].mag);
double delta = epsil * ((2 - alpha) / (1 + alpha));
double a;
if (delta < 0.00001) {
a = 2.0;
} else {
a = 2 * M_PI * delta * (1 - pow(delta, 2)) / sin(M_PI * delta);
}
// i_ipDFT starts here
/*i_ipDFT works well for higher reporting rates i.e. also Nr=25, but
e_ipDFT outperforms i_ipDFT for lower reporting rates (e.g. Nr=10)
i_ipDFT (variables definition) starts here*/
PhasorReIm phasor;
if (phasorRate > 10) {
phasor.r = Xk[km].r;
phasor.i = Xk[km].i;
PhasorReIm phasor_epsil = phasor;
PhasorReIm Xneg = phasor;
PhasorReIm Xneg_epsil = phasor;
phasor_epsil.r = Xk[km+epsil].r;
phasor_epsil.i = Xk[km+epsil].i;
double delta_old = delta;
// i_ipDFT
for (unsigned q = 0; q < P; q++) {
PhasorReIm hann_ft = hann_frt(delta + 2*(km+startBin-1), windowSize);
Xneg.r = 0.5*(phasor.r*hann_ft.r + phasor.i*hann_ft.i)*b;
Xneg.i = 0.5*(phasor.r*hann_ft.i - phasor.i*hann_ft.r)*b;
hann_ft = hann_frt(delta + epsil + 2*(km+startBin-1), windowSize);
Xneg_epsil.r = 0.5*(phasor.r*hann_ft.r + phasor.i*hann_ft.i)*b;
Xneg_epsil.i = 0.5*(phasor.r*hann_ft.i - phasor.i*hann_ft.r)*b;
phasor.r = phasor.r-Xneg.r;
phasor.i = phasor.i-Xneg.i;
phasor_epsil.r = phasor_epsil.r - Xneg_epsil.r;
phasor_epsil.i = phasor_epsil.i - Xneg_epsil.i;
Xk[km].mag = pow(pow(phasor.r, 2) + pow(phasor.i, 2), 0.5);
Xk[km+epsil].mag = pow(pow(phasor_epsil.r, 2) + pow(phasor_epsil.i, 2), 0.5);
alpha = abs(Xk[km].mag / Xk[km+epsil].mag);
delta = epsil*(2-alpha) / (1+alpha);
if (abs(delta - delta_old)==0){
q = P+1;
}
}
} else {
// end of i_ipDFT
/*e_ipDFT
e_ipDFT is very good from Nr=10 and Fs=10k; Not good otherwise.
Nonetheless, for Nr>=10 it presents better precision than i_ipDFT
*/
phasor.r = Xk[km].r;
phasor.i = Xk[km].i;
PhasorReIm v_ipdft;
v_ipdft.r = a*(Xk[km].r*cos(M_PI*delta)+Xk[km].i*sin(M_PI*delta));
v_ipdft.i = a*(-Xk[km].r*sin(M_PI*delta)+Xk[km].i*cos(M_PI*delta));
// This part is iterated P times
// variables allocation
PhasorReIm v1;
v1.r = v_ipdft.r;
v1.i = v_ipdft.i;
double e_delta_corr = delta;
std::vector<PhasorReIm> e_ipdft_3max;
for (unsigned k = 0; k < 3; k++) {
e_ipdft_3max.push_back({0., 0.});
e_ipdft_3max[k] = phasor;
}
e_ipdft_3max[0].r = Xk[km-1].r;
e_ipdft_3max[0].i = Xk[km-1].i;
e_ipdft_3max[1].r = Xk[km].r;
e_ipdft_3max[1].i = Xk[km].i;
e_ipdft_3max[2].r = Xk[km+1].r;
e_ipdft_3max[2].i = Xk[km+1].i;
std::vector<double> e_ipdft_3mag;
for (unsigned k = 0; k < 3; k++) {
e_ipdft_3mag.push_back(0.);
e_ipdft_3mag[k] = phasor.r;
}
PhasorReIm v_e_ipdft_max = phasor;
double e_a = phasor.r;
PhasorReIm hann_ft = phasor;
std::vector<PhasorReIm> e_ipdft_3max_new;
for (unsigned k = 0; k < 3; k++) {
e_ipdft_3max_new.push_back({0., 0.});
e_ipdft_3max_new[k] = phasor;
}
if (abs(delta) > 0) {
for (unsigned q = 0; q < P; q++) {
for (unsigned j = 0; j < 3; j++) {
hann_ft = hann_frt(j-2+e_delta_corr+2*(km+startBin), windowSize);
e_ipdft_3max_new[j].r = e_ipdft_3max[j].r-(v1.r*hann_ft.r + v1.i*hann_ft.i)*b;
e_ipdft_3max_new[j].i = e_ipdft_3max[j].i+(v1.i*hann_ft.r - v1.r*hann_ft.i)*b;
e_ipdft_3mag[j] = pow(pow(e_ipdft_3max_new[j].r, 2) + pow(e_ipdft_3max_new[j].i, 2), 0.5);
}
// interpolating the three bins to get the fractional correction term "delta_corr"
e_delta_corr = 2*epsil*(abs(e_ipdft_3mag[2]-e_ipdft_3mag[0]))/(e_ipdft_3mag[1]*2 + e_ipdft_3mag[0]+ e_ipdft_3mag[2]);
v_e_ipdft_max = e_ipdft_3max_new[1];
if (abs(e_delta_corr)<0.00001) {
e_delta_corr = 0;
v1.r = v_e_ipdft_max.r;
v1.i = v_e_ipdft_max.i;
q = P+1;
} else {
e_a = (1-pow(e_delta_corr, 2))*abs((M_PI*e_delta_corr)/sin(M_PI*e_delta_corr));
v1.r = e_a*(v_e_ipdft_max.r*cos(M_PI*e_delta_corr)+v_e_ipdft_max.i*sin(M_PI*e_delta_corr));
v1.i = e_a*(-v_e_ipdft_max.r*sin(M_PI*e_delta_corr)+v_e_ipdft_max.i*cos(M_PI*e_delta_corr));
}
}
phasor = v1;
delta = e_delta_corr;
}
}
// end e_ipDFT
fold = f;
Xk[km].f = (km + 1 + startBin + delta) * phasorRate;
if (fold > 0) {
dfold = df;
df = (f - fold)*phasorRate;
d2fold = d2f;
d2f = (d2f - d2fold)*phasorRate;
if (abs(df)>3 || abs(d2f>25 || state_rocof)) {
state_rocof = true;
rocof = 0.2043*df + 0.2043*dfold + 0.5913*rocof;
if (abs(rocof) < 0.035) {
state_rocof = false;
}
} else {
rocof = df;
}
}
if (abs(delta) < 0.00001) {
estimatedPhasor.amplitude = 2*Xk[km].mag;
} else {
estimatedPhasor.amplitude = 2*Xk[km].mag*M_PI*delta*(1-pow(delta, 2)) / sin(M_PI * delta);
}
estimatedPhasor.phase = atan2(Xk[km].i, Xk[km].r) - M_PI*delta;
estimatedPhasor.frequency = Xk[km].f;
estimatedPhasor.rocof = rocof;
if (lastPhasor.frequency !=
0) // Check if we already calculated a phasor before
estimatedPhasor.valid = Status::VALID;
return estimatedPhasor;
}
};
// Register hook
static char n[] = "truncated-ip-dft-pmu";
static char d[] = "This hook calculates a phasor based on truncated ipDFT";
static HookPlugin<TruncatedIpDftPmuHook, n, d,
(int)Hook::Flags::NODE_READ | (int)Hook::Flags::NODE_WRITE |
(int)Hook::Flags::PATH>
p;
} // namespace node
} // namespace villas