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ac_powerflow_lib.r
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ac_powerflow_lib.r
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ac_powerflow = function(
file_name,
v_fr = 1.0, v_to = 1.0,
vd_ub = 0.2, vd_lb = -0.2,
ad_ub = pi/6, ad_lb = -pi/6,
y_m = 1.0, y_a = -1.45,
t_m = 1.0, t_a = 0.0
) {
g = y_m*cos(y_a)
b = y_m*sin(y_a)
steps = 100
v_to_delta_lb = vd_lb + v_fr - v_to
v_to_delta_ub = vd_ub + v_fr - v_to
v_to_delta = seq(v_to_delta_lb, v_to_delta_ub, (v_to_delta_ub-v_to_delta_lb)/(steps-1))
vd_vals = (rep(v_to, steps) + v_to_delta) - rep(v_fr, steps)
ad_vals = seq(ad_lb, ad_ub, (ad_ub-ad_lb)/(steps-1))
stopifnot(vd_lb <= min(vd_vals)+0.000001)
stopifnot(vd_ub >= max(vd_vals)-0.000001)
pv = matrix(nrow = steps, ncol = steps)
qv = matrix(nrow = steps, ncol = steps)
for (i in 1:steps) {
v1 = v_fr;
v2 = v_to + v_to_delta[i];
for (j in 1:steps) {
ad = ad_vals[j];
pv[i,j] = g*v1^2/t_m^2 - g*v1/t_m*v2*cos(ad - t_a) - b*v1/t_m*v2*sin(ad - t_a)
qv[i,j] = -b*v1^2/t_m^2 + b*v1/t_m*v2*cos(ad - t_a) - g*v1/t_m*v2*sin(ad - t_a)
}
}
ps = 14
pdf(file_name, pointsize=ps, width=14, height=7, bg="white")
par(mfrow=c(1,2), oma=c(0,0,2.5,0))
contour(
x = vd_vals,
y = ad_vals,
pv,
#color = terrain.colors,
#levels = colorsteps,
nlevels = 8,
labcex=1.0,
plot.title = title(main = "Active Power (p)",
xlab = "Voltage Difference", ylab = "Angle Difference (rad)")
)
contour(
x = vd_vals,
y = ad_vals,
qv,
#color = terrain.colors,
#levels = colorsteps,
nlevels = 8,
labcex=1.0,
plot.title = title(main = "Reactive Power (q)",
xlab = "Voltage Difference", ylab = "Angle Difference (rad)")
)
title("AC Power Flow Fields (from side, p.u.)", outer=TRUE)
mtext(
sprintf("v1 = %.3f, g = %.3f, b = %.3f, tr = %.3f, as = %.3f", v_fr, g, b, t_m, t_a),
line=-1, outer=TRUE)
dev.off()
}
ac_powerloss = function(
file_name,
v_fr = 1.0, v_to = 1.0,
vd_ub = 0.2, vd_lb = -0.2,
ad_ub = pi/6, ad_lb = -pi/6,
y_m = 1.0, y_a = -1.45,
t_m = 1.0, t_a = 0.0
) {
g = y_m*cos(y_a)
b = y_m*sin(y_a)
steps = 100
v_to_delta_lb = vd_lb + v_fr - v_to
v_to_delta_ub = vd_ub + v_fr - v_to
v_to_delta = seq(v_to_delta_lb, v_to_delta_ub, (v_to_delta_ub-v_to_delta_lb)/(steps-1))
vd_vals = (rep(v_to, steps) + v_to_delta) - rep(v_fr, steps)
ad_vals = seq(ad_lb, ad_ub, (ad_ub-ad_lb)/(steps-1))
stopifnot(vd_lb <= min(vd_vals)+0.000001)
stopifnot(vd_ub >= max(vd_vals)-0.000001)
pv_fr = matrix(nrow = steps, ncol = steps)
qv_fr = matrix(nrow = steps, ncol = steps)
pv_to = matrix(nrow = steps, ncol = steps)
qv_to = matrix(nrow = steps, ncol = steps)
for (i in 1:steps) {
v1 = v_fr;
v2 = v_to + v_to_delta[i];
for (j in 1:steps) {
ad = ad_vals[j];
pv_fr[i,j] = g*v1^2/t_m^2 - g*v1/t_m*v2*cos(ad - t_a) - b*v1/t_m*v2*sin(ad - t_a)
qv_fr[i,j] = -b*v1^2/t_m^2 + b*v1/t_m*v2*cos(ad - t_a) - g*v1/t_m*v2*sin(ad - t_a)
pv_to[i,j] = g*v2^2 - g*v1/t_m*v2*cos(ad + t_a) - b*v1/t_m*v2*sin(ad + t_a)
qv_to[i,j] = -b*v2^2 + b*v1/t_m*v2*cos(ad + t_a) - g*v1/t_m*v2*sin(ad + t_a)
}
}
ps = 14
pdf(file_name, pointsize=ps, width=14, height=7, bg="white")
par(mfrow=c(1,2), oma=c(0,0,2.5,0))
contour(
x = vd_vals,
y = ad_vals,
pv_fr + pv_to,
#color = terrain.colors,
#levels = colorsteps,
nlevels = 8,
labcex=1.0,
plot.title = title(main = "Active Power (p)",
xlab = "Voltage Difference", ylab = "Angle Difference (rad)")
)
contour(
x = vd_vals,
y = ad_vals,
qv_fr + qv_to,
#color = terrain.colors,
#levels = colorsteps,
nlevels = 8,
labcex=1.0,
plot.title = title(main = "Reactive Power (q)",
xlab = "Voltage Difference", ylab = "Angle Difference (rad)")
)
title("AC Power Loss Fields (p.u.)", outer=TRUE)
mtext(
sprintf("v1 = %.3f, g = %.3f, b = %.3f, tr = %.3f, as = %.3f", v_fr, g, b, t_m, t_a),
line=-1, outer=TRUE)
dev.off()
}
ac_dc_comparison = function(
file_name,
v_fr = 1.0, v_to = 1.0,
ad_ub = 1.5*pi/2, ad_lb = -1.5*pi/2,
y_m = 1.0, y_a = -1.45,
t_m = 1.0, t_a = 0.0
) {
g = y_m*cos(y_a)
b = y_m*sin(y_a)
steps = 100
ad_vals = seq(ad_lb, ad_ub, (ad_ub-ad_lb)/(steps-1))
ac_p = rep(0.0, steps)
dc_p = rep(0.0, steps)
v1 = v_fr
v2 = v_to
for (i in 1:steps) {
ad = ad_vals[i];
ac_p[i] = g*v1^2/t_m^2 - g*v1/t_m*v2*cos(ad - t_a) - b*v1/t_m*v2*sin(ad - t_a)
dc_p[i] = -b*v1/t_m*v2*(ad - t_a)
}
ps = 16
pdf(file_name, pointsize=ps, width=7, height=7, bg="white")
x_range = c(min(ad_vals), max(ad_vals))
y_range = c(min(ac_p, dc_p), max(ac_p, dc_p))
plot(x_range, y_range, type="n", xlab = "Voltage Angle Difference (rad)", ylab = "Active Power (p.u.)", main="AC vs DC Active Power Comparison")
abline(h=0.0, col=rgb(0,0,0,0.5))
abline(v=0.0, col=rgb(0,0,0,0.5))
points(ad_vals, dc_p, type="l", lw=3, col="dodgerblue")
points(ad_vals, ac_p, type="l", lw=3, col="darkorange")
legend("topleft", legend=c("AC Power Flow", "DC Power Flow"), lty=1, lw=3, col=c("darkorange", "dodgerblue"), bg="white")
dev.off()
}