Segmentation¶

How to use time step segmentation to reduce the number of timesteps per period.

Author: Maximilian Hoffmann

In [1]:

%load_ext autoreload
%autoreload 2

import pandas as pd
import plotly.express as px
import plotly.io as pio

import tsam
from tsam import ClusterConfig, SegmentConfig

pio.renderers.default = "notebook_connected"
import warnings

# Added to every example notebook: silence the v3 column-order
# FutureWarning in the rendered docs (tsam v4 returns result columns in
# input order; see migration guide).
warnings.filterwarnings(
    "ignore", category=FutureWarning, message=".*sorted alphabetically.*"
)

%load_ext autoreload %autoreload 2 import pandas as pd import plotly.express as px import plotly.io as pio import tsam from tsam import ClusterConfig, SegmentConfig pio.renderers.default = "notebook_connected" import warnings # Added to every example notebook: silence the v3 column-order # FutureWarning in the rendered docs (tsam v4 returns result columns in # input order; see migration guide). warnings.filterwarnings( "ignore", category=FutureWarning, message=".*sorted alphabetically.*" )

Input data¶

In [2]:

raw = pd.read_csv("testdata.csv", index_col=0)

raw = pd.read_csv("testdata.csv", index_col=0)

10 typical days at hourly resolution (no segmentation)¶

Baseline: hierarchical clustering with medoid representation and 24 hourly timesteps.

In [3]:

result = tsam.aggregate(
    raw,
    n_clusters=10,
    period_duration=24,
    cluster=ClusterConfig(method="hierarchical"),
)
result.accuracy

result = tsam.aggregate( raw, n_clusters=10, period_duration=24, cluster=ClusterConfig(method="hierarchical"), ) result.accuracy

Out[3]:

AccuracyMetrics(
  rmse=0.1044 (weighted),
  mae=0.0715 (weighted),
  rmse_duration=0.0337 (weighted)
)

In [4]:

result.plot.cluster_members()

result.plot.cluster_members()

In [5]:

result.cluster_representatives

result.cluster_representatives

Out[5]:

		GHI	Load	T	Wind
	timestep
0	0	0.000000	383.795921	4.421453	5.043609
	1	0.000000	371.689230	4.026704	4.933965
	2	0.000000	374.310544	3.829330	4.714678
	3	0.000000	369.720991	3.730643	4.605034
	4	0.000000	376.053584	3.335894	5.591827
...	...	...	...	...	...
9	19	2.199516	478.910919	10.145308	2.192873
	20	0.000000	457.575577	10.342682	2.192873
	21	0.000000	444.225788	10.540056	2.192873
	22	0.000000	430.132842	10.441369	2.192873
	23	0.000000	401.874887	10.441369	2.192873

240 rows × 4 columns

20 typical days with 12 irregular segments¶

Segmentation reduces the number of timesteps per period while preserving key transitions.

In [6]:

result_segmented = tsam.aggregate(
    raw,
    n_clusters=20,
    period_duration=24,
    cluster=ClusterConfig(method="hierarchical"),
    segments=SegmentConfig(n_segments=12),
)
result_segmented.accuracy

result_segmented = tsam.aggregate( raw, n_clusters=20, period_duration=24, cluster=ClusterConfig(method="hierarchical"), segments=SegmentConfig(n_segments=12), ) result_segmented.accuracy

Out[6]:

AccuracyMetrics(
  rmse=0.0961 (weighted),
  mae=0.0658 (weighted),
  rmse_duration=0.0203 (weighted)
)

In [7]:

result_segmented.plot.cluster_members()

result_segmented.plot.cluster_members()

In [8]:

result_segmented.plot.segment_durations()

result_segmented.plot.segment_durations()

In [9]:

result_segmented.cluster_representatives

result_segmented.cluster_representatives

Out[9]:

			GHI	Load	T	Wind
	Segment Step	Segment Duration
0	0	4	0.000000	403.310708	1.025025	2.226777
	1	2	0.000000	424.393351	1.122830	3.340165
	2	1	0.000000	495.118712	1.171733	3.340165
	3	2	11.182790	541.665766	1.562953	3.340165
	4	4	74.551932	547.697631	2.272040	2.226777
...	...	...	...	...	...	...
19	7	3	76.681988	471.099097	-2.447057	3.340165
	8	4	34.080883	469.022225	-1.664616	2.226777
	9	1	0.000000	499.029025	-2.055836	2.226777
	10	4	0.000000	498.349573	-2.178093	1.113388
	11	2	0.000000	474.908494	-2.495959	2.226777

240 rows × 4 columns

Comparison¶

In [10]:

results = {
    "10 x 24h": result,
    "20 x 12seg": result_segmented,
}

# Duration curves
frames = []
for name, r in {"Original": None, **results}.items():
    vals = (raw if r is None else r.reconstructed)["Load"]
    sorted_vals = vals.sort_values(ascending=False).reset_index(drop=True)
    frames.append(
        pd.DataFrame(
            {"Hour": range(len(sorted_vals)), "Load": sorted_vals, "Method": name}
        )
    )

px.line(
    pd.concat(frames, ignore_index=True),
    x="Hour",
    y="Load",
    color="Method",
    title="Duration Curve Comparison - Load",
)

results = { "10 x 24h": result, "20 x 12seg": result_segmented, } # Duration curves frames = [] for name, r in {"Original": None, **results}.items(): vals = (raw if r is None else r.reconstructed)["Load"] sorted_vals = vals.sort_values(ascending=False).reset_index(drop=True) frames.append( pd.DataFrame( {"Hour": range(len(sorted_vals)), "Load": sorted_vals, "Method": name} ) ) px.line( pd.concat(frames, ignore_index=True), x="Hour", y="Load", color="Method", title="Duration Curve Comparison - Load", )

In [11]:

# Heatmap comparison
param = "GHI"

import plotly.graph_objects as go
from plotly.subplots import make_subplots

labels = ["Original", "10 x 24h", "20 x 12seg"]
data = [
    tsam.unstack_to_periods(raw, period_duration=24),
    tsam.unstack_to_periods(result.reconstructed, period_duration=24),
    tsam.unstack_to_periods(result_segmented.reconstructed, period_duration=24),
]

fig = make_subplots(rows=3, cols=1, subplot_titles=labels, vertical_spacing=0.05)
for i, d in enumerate(data, 1):
    fig.add_trace(go.Heatmap(z=d[param].values.T, coloraxis="coloraxis"), row=i, col=1)
fig.update_layout(
    height=750,
    coloraxis={"colorscale": "Viridis"},
    title_text=f"Heatmap Comparison - {param}",
)
fig.show()

# Heatmap comparison param = "GHI" import plotly.graph_objects as go from plotly.subplots import make_subplots labels = ["Original", "10 x 24h", "20 x 12seg"] data = [ tsam.unstack_to_periods(raw, period_duration=24), tsam.unstack_to_periods(result.reconstructed, period_duration=24), tsam.unstack_to_periods(result_segmented.reconstructed, period_duration=24), ] fig = make_subplots(rows=3, cols=1, subplot_titles=labels, vertical_spacing=0.05) for i, d in enumerate(data, 1): fig.add_trace(go.Heatmap(z=d[param].values.T, coloraxis="coloraxis"), row=i, col=1) fig.update_layout( height=750, coloraxis={"colorscale": "Viridis"}, title_text=f"Heatmap Comparison - {param}", ) fig.show()

In [12]:

# Time slice comparison
frames = []
for name, r in {"Original": None, **results}.items():
    df = raw if r is None else r.reconstructed
    sliced = df.loc["20100210":"20100218", ["Load"]].copy()
    sliced["Method"] = name
    frames.append(sliced)

px.line(
    pd.concat(frames).reset_index(names="Time"),
    x="Time",
    y="Load",
    color="Method",
    title="Time Slice Comparison - Load (Feb 10-18)",
)

# Time slice comparison frames = [] for name, r in {"Original": None, **results}.items(): df = raw if r is None else r.reconstructed sliced = df.loc["20100210":"20100218", ["Load"]].copy() sliced["Method"] = name frames.append(sliced) px.line( pd.concat(frames).reset_index(names="Time"), x="Time", y="Load", color="Method", title="Time Slice Comparison - Load (Feb 10-18)", )

Validation¶

Column means should be preserved for both approaches.

In [13]:

means = pd.DataFrame(
    {
        "Original": raw.mean(),
        "10 x 24h": result.reconstructed.mean(),
        "20 x 12seg": result_segmented.reconstructed.mean(),
    }
)
means

means = pd.DataFrame( { "Original": raw.mean(), "10 x 24h": result.reconstructed.mean(), "20 x 12seg": result_segmented.reconstructed.mean(), } ) means

Out[13]:

	Original	10 x 24h	20 x 12seg
GHI	110.990183	110.990183	110.990179
Load	450.260335	450.260335	450.260335
T	7.790616	7.790616	7.790616
Wind	3.057306	3.057306	3.057306