EBG-671_bo_problems

EBG-671_bo_problems.ipynb

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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This notebook shows an undesiderate effect of the Bid Optimization algorithm implemented in eneberg-forecast. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sys\n",
      "sys.path.append('../../bin')\n",
      "from lib.BidOptimisation import BidOptimisation as BO\n",
      "from scipy.stats import norm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "params = {\n",
      "\"spot_price\": 14.0,\n",
      "\"avoidable_cost\": 8.0,\n",
      "\"premium_price\": 1.0,\n",
      "\"imbalance_cost_under3\": 16.86,\n",
      "\"imbalance_cost_over3\": 48.45,\n",
      "\"imbalance_income_under3\": 11.9,\n",
      "\"fuel_cost_adjustment\": 1.0,\n",
      "\"exp_imbalance_rate\": 0.0,\n",
      "\"exp_imbalance_rate_std\": 10.0\n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 199
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def get_correlation(bid):\n",
      "    \"\"\"\n",
      "    This function replicates the method BidOptimisation.bid_optimisation()\n",
      "    \"\"\"\n",
      "    step_size = 0.001\n",
      "    x = np.arange(-2.0, 2.0, step_size)\n",
      "    err_dvalue = bid._err_pdf(x)\n",
      "    prof_value = bid._profit_at_error(x)\n",
      "    adj = np.arange(-(len(x)-1), len(x), 1.0) * step_size\n",
      "    profit_by_adj = np.correlate(prof_value, err_dvalue, 'full')\n",
      "    profit_by_adj *= step_size\n",
      "    best_adjustment = np.array([adj[np.argmax(profit_by_adj)]*100.0])\n",
      "    # plotting not included in the original method\n",
      "    hlines(0.0,min(adj),max(adj),alpha=.5)\n",
      "    plot(adj,profit_by_adj)\n",
      "    ylabel('expected profit')\n",
      "    xlabel('adjustment')\n",
      "    print np.sum(prof_value <= 0.0),' profit samples are less than zero, out of', len(prof_value)\n",
      "    print np.sum(profit_by_adj <= 0.0),' expected profit samples are less than zero, out of', len(profit_by_adj)\n",
      "    print 'adjustment returned:',best_adjustment/100.0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 194
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The current BidOptimization algorithm does the following operations:\n",
      "```\n",
      "expected_profit = []\n",
      "for adj in adjustments_to_try:\n",
      " - multiply the profit_curve by the error distribution\n",
      " - save the result in expected_profit\n",
      "return the adjustment that gave the best expected profit\n",
      "```\n",
      "Unfortunately, there are some conditions that make the algorithm return an indesiderate result. The conditions identified are two:\n",
      "\n",
      "1. The spot price is too low. (which means that the profit curve is too low)\n",
      "2. The standard deviation of the error distribution is too large.\n",
      "\n",
      "In condition 1 happens we have that the trading conditions are not favorable. In condition 2 we have that the result of the eneberg forecast is unreliable.\n",
      "\n",
      "In both cases the expected profit is always less than 0, and 0 with a particularly extreme adjustment.\n",
      "\n",
      "The following charts show the expected profit in the two situations."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*** case 1 ***"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "params['spot_price'] = 9.10\n",
      "get_correlation(BO(**params))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3934  profit samples are less than zero, out of 4000\n",
        "7999  expected profit samples are less than zero, out of 7999\n",
        "adjustment returned: [-3.999]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10e6d9ed0>"
       ]
      }
     ],
     "prompt_number": 201
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*** case 2 ***"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "params['spot_price'] = 15.0\n",
      "params[\"exp_imbalance_rate_std\"] = 55.0\n",
      "get_correlation(BO(**params))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3119  profit samples are less than zero, out of 4000\n",
        "7999  expected profit samples are less than zero, out of 7999\n",
        "adjustment returned: [-3.999]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10e6cb050>"
       ]
      }
     ],
     "prompt_number": 202
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In both cases, the algorithm returned the first adjustment tried (-399%). "
     ]
    }
   ],
   "metadata": {}
  }
 ]
}