HighChart - Group data by day

You can achieve the desired look by using dataGrouping. That way you don't have to do any extra processing. All you would need to do, is to give this definition:

plotOptions: {
  series: {
    dataGrouping: {
      forced: true,
      units: [
        ['day', [1]]
      ]
    }
  }
},

To get the actual time of the point in the tooltip you could then do this:

tooltip: {
  pointFormatter: function() {
    var n = this.series.name;
    var s = '<span style="color:' + this.series.color + '">' + this.series.name + '</span>: <b>';
    return Highcharts.dateFormat('%m/%d - %H:%M', this.series.xData[this.index]) + s + Highcharts.numberFormat((this.y / 1000), 2, '.') + ' kV</b><br/>';
  }
},

Where Highcharts.dateFormat('%m/%d - %H:%M', this.series.xData[this.index]) gets the actual time of the point.

Working JSFiddle Example: http://jsfiddle.net/ewolden/omfdy8nc/

API on dataGrouping: https://api.highcharts.com/highstock/series.line.dataGrouping

To remove the extra time that can be in front or after the series when dataGrouping is done per day we need to set a min and max value. The reason we have this whitespace is because the original data have values that are not exactly set at midnight per day.

Adding the following load event will find the minumum/maximum full day and set the xAxis and the navigator xAxis to these values:

chart: {
  events: {
    load: function() {
      let extremes = this.xAxis[0].getExtremes()
      let min = extremes.dataMin - extremes.dataMin % (1000 * 60 * 60 * 24),
        max = extremes.dataMax - extremes.dataMax % (1000 * 60 * 60 * 24);
      this.update({
        xAxis: {
          min: min,
          max: max
        },
        navigator: {
          xAxis: {
            min: min,
            max: max
          }
        }
      }, true, false, false)
    }
  }
},

Working example: http://jsfiddle.net/ewolden/omfdy8nc/32/

API on the load event: https://api.highcharts.com/highstock/chart.events.load

API on chart.update: https://api.highcharts.com/class-reference/Highcharts.Chart#update

You can use the same timestamp for each point on the same day as x property and save the real timestamp in the point object for example as realX. Then use real timestamp in tooltip.pointFormatter to create show the real date for each point. Check the example posted below.

HTML:

<script src="https://code.highcharts.com/stock/highstock.js"></script>
<script src="https://code.highcharts.com/stock/modules/exporting.js"></script>

<div id="container" style="min-width: 310px; height: 400px; margin: 0 auto"></div>

JS:

var data = [{
    name: "Minima",
    pointInterval: 86400000,
    data: [
      [1538467200000, 215.9],
      [1538581500000, 217.6],
      [1538651700000, 218],
      [1538728200000, 218.5]
    ]
  }, {
    name: "Maxima",
    pointInterval: 86400000,
    data: [
      [1538506800000, 228.8],
      [1538530200000, 228.4],
      [1538676000000, 229.3],
      [1538779500000, 228.8]
    ]
  }, {
    name: "Promedio",
    pointInterval: 86400000,
    data: [
      [1538438400000, 223.9365],
      [1538524800000, 224.0667],
      [1538611200000, 224.4135],
      [1538697600000, 224.45]
    ]
  }],
  finalData = [],
  i,
  j,
  series,
  point;

for (i = 0; i < data.length; i++) {
  series = data[i];
  finalData[i] = {
    name: series.name,
    pointInterval: series.pointInterval,
    data: []
  };

  for (j = 0; j < series.data.length; j++) {
    point = series.data[j];

    finalData[i].data.push({
      x: data[0].data[j][0],
      y: point[1],
      realX: point[0]
    });
  }
}

chart = new Highcharts.StockChart({

  chart: {
    renderTo: "container",
    type: 'spline'
  },

  colors: ['#3131F8', '#FB1C1C', '#008000', '#f7a35c', '#8085e9',
    '#f15c80', '#e4d354', '#8085e8', '#8d4653', '#91e8e1'
  ],

  yAxis: {
    opposite: false,
    showLastLabel: true,
    labels: {
      enabled: true,
      align: "right"
    },

    title: {
      text: 'Tensión'
    }
  },

  rangeSelector: {
    enabled: true
  },

  tooltip: {
    pointFormatter: function() {
      var n = this.series.name,
        s = '<span style="color:' + this.series.color + '">' + n + '</span>: <b>',
        date = 'Date: ' + Highcharts.dateFormat('%e. %b %H:%M', this.realX),
        number = Highcharts.numberFormat((this.y / 1000), 2, '.') + ' kV</b><br/>';
      return s + number + date;
    }
  },

  legend: {
    enabled: true
  },

  navigation: {
    buttonOptions: {
      enabled: true
    }
  },

  series: finalData
});

Demo: https://jsfiddle.net/BlackLabel/qfv1yzmh/1/