{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# Load flow calculation with distributed slack" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In power flow analysis, a slack bus is chosen which compensates the mismatch of active power in the grid as related to the balance of consumption, generation and losses. This mismatch results from grid losses or an unbalanced dispatch. In real transmission and distribution systems, multiple generators can play a role in compensating the mismatch of active power. The approach of _distributed slack_ allows to model the allocation of the mismatch compensation to a number of buses according to pre-defined weights, which more closely resembles real-world scenarios. To describe how much active power a single element contributes to the compensation of the mismatch of active power, the parameter *slack_weight* is used. \n", "\n", "In pandapower, the load flow calculation with Newton-Raphson algorithm supports the functionality of distributed slack. To this end, the user can set the argument *distributed_slack* to True when calling the function runpp. The slack weights for *ext_grid*, *gen* and *xward* elements should be provided in the *slack_weight* column." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### How the slack weight is considered\n", "The sum of all slack weights of the contributing elements should be 1 and must be greater than 0. If the sum of the slack weights is other than 1, it is normalized to 1 before the load flow calculation. If the net has exactly one slack, e.g. an ext_grid, and only this element has a slack_weight other than 0, a load flow calculation considering distributed slack will have the same results as a load flow calculation without using the distributed slack (details in the first example below)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### How the active power mismatch is attributed to the elements\n", "The resulting active power of an element $i$ after the load flow calculation with distributed slack can be represented as follows ($ng$: number of generation plants, $nc$: number of consumptions, $nb$: number of branches):\n", "\n", "\n", "$$P_{result,i}= P_{set,i} - (\\sum_{elm=1}^{ng}P_{generation,elm} - \\sum_{elm=1}^{nc}P_{consumption,elm} - \\sum_{branch=1}^{nb}P_{losses,branch}) \\cdot slack\\_weight_i$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculation example\n", "We import necessary modules and create an example grid model:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "/* global mpl */\n", "window.mpl = {};\n", "\n", "mpl.get_websocket_type = function () {\n", " if (typeof WebSocket !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof MozWebSocket !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert(\n", " 'Your browser does not have WebSocket support. 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toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", " /* Instead of a spacer, we start a new button group. */\n", " if (buttonGroup.hasChildNodes()) {\n", " toolbar.appendChild(buttonGroup);\n", " }\n", " buttonGroup = document.createElement('div');\n", " buttonGroup.classList = 'mpl-button-group';\n", " continue;\n", " }\n", "\n", " var button = (fig.buttons[name] = document.createElement('button'));\n", " button.classList = 'mpl-widget';\n", " button.setAttribute('role', 'button');\n", " button.setAttribute('aria-disabled', 'false');\n", " button.addEventListener('click', on_click_closure(method_name));\n", " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", "\n", " var icon_img = document.createElement('img');\n", " icon_img.src = '_images/' + image + '.png';\n", " icon_img.srcset = '_images/' + image + '_large.png 2x';\n", " icon_img.alt = tooltip;\n", " button.appendChild(icon_img);\n", "\n", " buttonGroup.appendChild(button);\n", " }\n", "\n", " if (buttonGroup.hasChildNodes()) {\n", " toolbar.appendChild(buttonGroup);\n", " }\n", "\n", " var fmt_picker = document.createElement('select');\n", " fmt_picker.classList = 'mpl-widget';\n", " toolbar.appendChild(fmt_picker);\n", " this.format_dropdown = fmt_picker;\n", "\n", " for (var ind in mpl.extensions) {\n", " var fmt = mpl.extensions[ind];\n", " var option = document.createElement('option');\n", " option.selected = fmt === mpl.default_extension;\n", " option.innerHTML = fmt;\n", " fmt_picker.appendChild(option);\n", " }\n", "\n", " var status_bar = document.createElement('span');\n", " status_bar.classList = 'mpl-message';\n", " toolbar.appendChild(status_bar);\n", " this.message = status_bar;\n", "};\n", "\n", "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n", " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", " // which will in turn request a refresh of the image.\n", " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", "};\n", "\n", "mpl.figure.prototype.send_message = function (type, properties) {\n", " properties['type'] = type;\n", " properties['figure_id'] = this.id;\n", " this.ws.send(JSON.stringify(properties));\n", "};\n", "\n", "mpl.figure.prototype.send_draw_message = function () {\n", " if (!this.waiting) {\n", " this.waiting = true;\n", " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", " var format_dropdown = fig.format_dropdown;\n", " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", " fig.ondownload(fig, format);\n", "};\n", "\n", "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", " var size = msg['size'];\n", " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", " fig._resize_canvas(size[0], size[1], msg['forward']);\n", " fig.send_message('refresh', {});\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", " var x0 = msg['x0'] / fig.ratio;\n", " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", " var x1 = msg['x1'] / fig.ratio;\n", " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0,\n", " 0,\n", " fig.canvas.width / fig.ratio,\n", " fig.canvas.height / fig.ratio\n", " );\n", "\n", " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", "};\n", "\n", "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", " // Updates the figure title.\n", " fig.header.textContent = msg['label'];\n", "};\n", "\n", "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", " fig.rubberband_canvas.style.cursor = msg['cursor'];\n", "};\n", "\n", "mpl.figure.prototype.handle_message = function (fig, msg) {\n", " fig.message.textContent = msg['message'];\n", "};\n", "\n", "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", " // Request the server to send over a new figure.\n", " fig.send_draw_message();\n", "};\n", "\n", "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", " fig.image_mode = msg['mode'];\n", "};\n", "\n", "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", " for (var key in msg) {\n", " if (!(key in fig.buttons)) {\n", " continue;\n", " }\n", " fig.buttons[key].disabled = !msg[key];\n", " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", " if (msg['mode'] === 'PAN') {\n", " fig.buttons['Pan'].classList.add('active');\n", " fig.buttons['Zoom'].classList.remove('active');\n", " } else if (msg['mode'] === 'ZOOM') {\n", " fig.buttons['Pan'].classList.remove('active');\n", " fig.buttons['Zoom'].classList.add('active');\n", " } else {\n", " fig.buttons['Pan'].classList.remove('active');\n", " fig.buttons['Zoom'].classList.remove('active');\n", " }\n", "};\n", "\n", "mpl.figure.prototype.updated_canvas_event = function () {\n", " // Called whenever the canvas gets updated.\n", " this.send_message('ack', {});\n", "};\n", "\n", "// A function to construct a web socket function for onmessage handling.\n", "// Called in the figure constructor.\n", "mpl.figure.prototype._make_on_message_function = function (fig) {\n", " return function socket_on_message(evt) {\n", " if (evt.data instanceof Blob) {\n", " var img = evt.data;\n", " if (img.type !== 'image/png') {\n", " /* FIXME: We get \"Resource interpreted as Image but\n", " * transferred with MIME type text/plain:\" errors on\n", " * Chrome. But how to set the MIME type? It doesn't seem\n", " * to be part of the websocket stream */\n", " img.type = 'image/png';\n", " }\n", "\n", " /* Free the memory for the previous frames */\n", " if (fig.imageObj.src) {\n", " (window.URL || window.webkitURL).revokeObjectURL(\n", " fig.imageObj.src\n", " );\n", " }\n", "\n", " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", " img\n", " );\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " } else if (\n", " typeof evt.data === 'string' &&\n", " evt.data.slice(0, 21) === 'data:image/png;base64'\n", " ) {\n", " fig.imageObj.src = evt.data;\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " }\n", "\n", " var msg = JSON.parse(evt.data);\n", " var msg_type = msg['type'];\n", "\n", " // Call the \"handle_{type}\" callback, which takes\n", " // the figure and JSON message as its only arguments.\n", " try {\n", " var callback = fig['handle_' + msg_type];\n", " } catch (e) {\n", " console.log(\n", " \"No handler for the '\" + msg_type + \"' message type: \",\n", " msg\n", " );\n", " return;\n", " }\n", "\n", " if (callback) {\n", " try {\n", " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", " callback(fig, msg);\n", " } catch (e) {\n", " console.log(\n", " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", " e,\n", " e.stack,\n", " msg\n", " );\n", " }\n", " }\n", " };\n", "};\n", "\n", "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", "mpl.findpos = function (e) {\n", " //this section is from http://www.quirksmode.org/js/events_properties.html\n", " var targ;\n", " if (!e) {\n", " e = window.event;\n", " }\n", " if (e.target) {\n", " targ = e.target;\n", " } else if (e.srcElement) {\n", " targ = e.srcElement;\n", " }\n", " if (targ.nodeType === 3) {\n", " // defeat Safari bug\n", " targ = targ.parentNode;\n", " }\n", "\n", " // pageX,Y are the mouse positions relative to the document\n", " var boundingRect = targ.getBoundingClientRect();\n", " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", "\n", " return { x: x, y: y };\n", "};\n", "\n", "/*\n", " * return a copy of an object with only non-object keys\n", " * we need this to avoid circular references\n", " * https://stackoverflow.com/a/24161582/3208463\n", " */\n", "function simpleKeys(original) {\n", " return Object.keys(original).reduce(function (obj, key) {\n", " if (typeof original[key] !== 'object') {\n", " obj[key] = original[key];\n", " }\n", " return obj;\n", " }, {});\n", "}\n", "\n", "mpl.figure.prototype.mouse_event = function (event, name) {\n", " var canvas_pos = mpl.findpos(event);\n", "\n", " if (name === 'button_press') {\n", " this.canvas.focus();\n", " this.canvas_div.focus();\n", " }\n", "\n", " var x = canvas_pos.x * this.ratio;\n", " var y = canvas_pos.y * this.ratio;\n", "\n", " this.send_message(name, {\n", " x: x,\n", " y: y,\n", " button: event.button,\n", " step: event.step,\n", " guiEvent: simpleKeys(event),\n", " });\n", "\n", " /* This prevents the web browser from automatically changing to\n", " * the text insertion cursor when the button is pressed. We want\n", " * to control all of the cursor setting manually through the\n", " * 'cursor' event from matplotlib */\n", " event.preventDefault();\n", " return false;\n", "};\n", "\n", "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", " // Handle any extra behaviour associated with a key event\n", "};\n", "\n", "mpl.figure.prototype.key_event = function (event, name) {\n", " // Prevent repeat events\n", " if (name === 'key_press') {\n", " if (event.key === this._key) {\n", " return;\n", " } else {\n", " this._key = event.key;\n", " }\n", " }\n", " if (name === 'key_release') {\n", " this._key = null;\n", " }\n", "\n", " var value = '';\n", " if (event.ctrlKey && event.key !== 'Control') {\n", " value += 'ctrl+';\n", " }\n", " else if (event.altKey && event.key !== 'Alt') {\n", " value += 'alt+';\n", " }\n", " else if (event.shiftKey && event.key !== 'Shift') {\n", " value += 'shift+';\n", " }\n", "\n", " value += 'k' + event.key;\n", "\n", " this._key_event_extra(event, name);\n", "\n", " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", " return false;\n", "};\n", "\n", "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", " if (name === 'download') {\n", " this.handle_save(this, null);\n", " } else {\n", " this.send_message('toolbar_button', { name: name });\n", " }\n", "};\n", "\n", "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", " this.message.textContent = tooltip;\n", "};\n", "\n", "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n", "// prettier-ignore\n", "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n", "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", "\n", "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", "\n", "mpl.default_extension = \"png\";/* global mpl */\n", "\n", "var comm_websocket_adapter = function (comm) {\n", " // Create a \"websocket\"-like object which calls the given IPython comm\n", " // object with the appropriate methods. 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\");\n", " if (!fig.cell_info) {\n", " console.error('Failed to find cell for figure', id, fig);\n", " return;\n", " }\n", " fig.cell_info[0].output_area.element.on(\n", " 'cleared',\n", " { fig: fig },\n", " fig._remove_fig_handler\n", " );\n", "};\n", "\n", "mpl.figure.prototype.handle_close = function (fig, msg) {\n", " var width = fig.canvas.width / fig.ratio;\n", " fig.cell_info[0].output_area.element.off(\n", " 'cleared',\n", " fig._remove_fig_handler\n", " );\n", " fig.resizeObserverInstance.unobserve(fig.canvas_div);\n", "\n", " // Update the output cell to use the data from the current canvas.\n", " fig.push_to_output();\n", " var dataURL = fig.canvas.toDataURL();\n", " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", " // the notebook keyboard shortcuts fail.\n", " IPython.keyboard_manager.enable();\n", " fig.parent_element.innerHTML =\n", " '';\n", " fig.close_ws(fig, msg);\n", "};\n", "\n", "mpl.figure.prototype.close_ws = function (fig, msg) {\n", " fig.send_message('closing', msg);\n", " // fig.ws.close()\n", "};\n", "\n", "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", " // Turn the data on the canvas into data in the output cell.\n", " var width = this.canvas.width / this.ratio;\n", " var dataURL = this.canvas.toDataURL();\n", " this.cell_info[1]['text/html'] =\n", " '';\n", "};\n", "\n", "mpl.figure.prototype.updated_canvas_event = function () {\n", " // Tell IPython that the notebook contents must change.\n", " IPython.notebook.set_dirty(true);\n", " this.send_message('ack', {});\n", " var fig = this;\n", " // Wait a second, then push the new image to the DOM so\n", " // that it is saved nicely (might be nice to debounce this).\n", " setTimeout(function () {\n", " fig.push_to_output();\n", " }, 1000);\n", "};\n", "\n", "mpl.figure.prototype._init_toolbar = function () {\n", " var fig = this;\n", "\n", " var toolbar = document.createElement('div');\n", " toolbar.classList = 'btn-toolbar';\n", " this.root.appendChild(toolbar);\n", "\n", " function on_click_closure(name) {\n", " return function (_event) {\n", " return fig.toolbar_button_onclick(name);\n", " };\n", " }\n", "\n", " function on_mouseover_closure(tooltip) {\n", " return function (event) {\n", " if (!event.currentTarget.disabled) {\n", " return fig.toolbar_button_onmouseover(tooltip);\n", " }\n", " };\n", " }\n", "\n", " fig.buttons = {};\n", " var buttonGroup = document.createElement('div');\n", " buttonGroup.classList = 'btn-group';\n", " var button;\n", " for (var toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", " /* Instead of a spacer, we start a new button group. */\n", " if (buttonGroup.hasChildNodes()) {\n", " toolbar.appendChild(buttonGroup);\n", " }\n", " buttonGroup = document.createElement('div');\n", " buttonGroup.classList = 'btn-group';\n", " continue;\n", " }\n", "\n", " button = fig.buttons[name] = document.createElement('button');\n", " button.classList = 'btn btn-default';\n", " button.href = '#';\n", " button.title = name;\n", " button.innerHTML = '';\n", " button.addEventListener('click', on_click_closure(method_name));\n", " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", " buttonGroup.appendChild(button);\n", " }\n", "\n", " if (buttonGroup.hasChildNodes()) {\n", " toolbar.appendChild(buttonGroup);\n", " }\n", "\n", " // Add the status bar.\n", " var status_bar = document.createElement('span');\n", " status_bar.classList = 'mpl-message pull-right';\n", " toolbar.appendChild(status_bar);\n", " this.message = status_bar;\n", "\n", " // Add the close button to the window.\n", " var buttongrp = document.createElement('div');\n", " buttongrp.classList = 'btn-group inline pull-right';\n", " button = document.createElement('button');\n", " button.classList = 'btn btn-mini btn-primary';\n", " button.href = '#';\n", " button.title = 'Stop Interaction';\n", " button.innerHTML = '';\n", " button.addEventListener('click', function (_evt) {\n", " fig.handle_close(fig, {});\n", " });\n", " button.addEventListener(\n", " 'mouseover',\n", " on_mouseover_closure('Stop Interaction')\n", " );\n", " buttongrp.appendChild(button);\n", " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", "};\n", "\n", "mpl.figure.prototype._remove_fig_handler = function (event) {\n", " var fig = event.data.fig;\n", " if (event.target !== this) {\n", " // Ignore bubbled events from children.\n", " return;\n", " }\n", " fig.close_ws(fig, {});\n", "};\n", "\n", "mpl.figure.prototype._root_extra_style = function (el) {\n", " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", "};\n", "\n", "mpl.figure.prototype._canvas_extra_style = function (el) {\n", " // this is important to make the div 'focusable\n", " el.setAttribute('tabindex', 0);\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", " } else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", "};\n", "\n", "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", " // Check for shift+enter\n", " if (event.shiftKey && event.which === 13) {\n", " this.canvas_div.blur();\n", " // select the cell after this one\n", " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", " IPython.notebook.select(index + 1);\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", " fig.ondownload(fig, null);\n", "};\n", "\n", "mpl.find_output_cell = function (html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", " for (var i = 0; i < ncells; i++) {\n", " var cell = cells[i];\n", " if (cell.cell_type === 'code') {\n", " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", " var data = cell.output_area.outputs[j];\n", " if (data.data) {\n", " // IPython >= 3 moved mimebundle to data attribute of output\n", " data = data.data;\n", " }\n", " if (data['text/html'] === html_output) {\n", " return [cell, data, j];\n", " }\n", " }\n", " }\n", " }\n", "};\n", "\n", "// Register the function which deals with the matplotlib target/channel.\n", "// The kernel may be null if the page has been refreshed.\n", "if (IPython.notebook.kernel !== null) {\n", " IPython.notebook.kernel.comm_manager.register_target(\n", " 'matplotlib',\n", " mpl.mpl_figure_comm\n", " );\n", "}\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# configures the rendering and features of plots which use matplotlib:\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "%matplotlib notebook\n", "\n", "from copy import deepcopy\n", "import pandapower as pp\n", "import pandapower.plotting\n", "from pandapower import networks as nw\n", "\n", "from IPython.display import display, Markdown\n", "\n", "net = nw.case9()\n", "fig = plt.figure(figsize=(4,4))\n", "ax = fig.add_subplot()\n", "pp.plotting.simple_plot(net, plot_loads=True, plot_gens=True, load_size=2.5, gen_size=0.1, ax=ax);\n", "fig.tight_layout(pad=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## First example: distributed slack with just the ext_grid element\n", "In each case, we first define the contributing elements and their slack weights. Then we compare the results of the load flow calculation with and without the distributed slack calculation." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def print_powers(net):\n", " print(f\"Consumption of loads:\\t\\t\\t {net.load.at[0, 'p_mw']:>6.2f} MW\\t {net.load.at[1, 'p_mw']:>6.2f} MW\\t {net.load.at[2, 'p_mw']:>6.2f} MW\\t ({net.load.p_mw.sum():>6.2f} MW total)\")\n", " print(f\"Injection of generators (input):\\t {net.gen.at[0, 'p_mw']:>6.2f} MW\\t {net.gen.at[1, 'p_mw']:>6.2f} MW\\t\\t\\t ({net.gen.p_mw.sum():>6.2f} MW total)\")\n", " print(f\"Injection of generators (results):\\t {net.res_gen.at[0, 'p_mw']:>6.2f} MW\\t {net.res_gen.at[1, 'p_mw']:>6.2f} MW\\t\\t\\t ({net.res_gen.p_mw.sum():>6.2f} MW total)\")\n", " print(f\"Injection of generators (difference):\\t {net.res_gen.at[0, 'p_mw']-net.gen.at[0, 'p_mw']:>6.2f} MW\\t {net.res_gen.at[1, 'p_mw']-net.gen.at[1, 'p_mw']:>6.2f} MW\\t\\t\\t ({net.res_gen.p_mw.sum()-net.gen.p_mw.sum():>6.2f} MW total)\")\n", " print(f\"Slack power at ext_grid (results):\\t {net.res_ext_grid.at[0, 'p_mw']:>6.2f} MW\")\n", " print(f\"Line losses (results):\\t\\t\\t {net.res_line.pl_mw.sum():>6.2f} MW\")" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Without distributed slack" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Consumption of loads:\t\t\t 90.00 MW\t 100.00 MW\t 125.00 MW\t (315.00 MW total)\n", "Injection of generators (input):\t 163.00 MW\t 85.00 MW\t\t\t (248.00 MW total)\n", "Injection of generators (results):\t 163.00 MW\t 85.00 MW\t\t\t (248.00 MW total)\n", "Injection of generators (difference):\t 0.00 MW\t 0.00 MW\t\t\t ( 0.00 MW total)\n", "Slack power at ext_grid (results):\t 71.95 MW\n", "Line losses (results):\t\t\t 4.95 MW\n" ] }, { "data": { "text/markdown": [ "#### With distributed slack" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Consumption of loads:\t\t\t 90.00 MW\t 100.00 MW\t 125.00 MW\t (315.00 MW total)\n", "Injection of generators (input):\t 163.00 MW\t 85.00 MW\t\t\t (248.00 MW total)\n", "Injection of generators (results):\t 163.00 MW\t 85.00 MW\t\t\t (248.00 MW total)\n", "Injection of generators (difference):\t 0.00 MW\t 0.00 MW\t\t\t ( 0.00 MW total)\n", "Slack power at ext_grid (results):\t 71.95 MW\n", "Line losses (results):\t\t\t 4.95 MW\n" ] } ], "source": [ "display(Markdown(\"#### Without distributed slack\"))\n", "pp.runpp(net)\n", "\n", "print_powers(net)\n", "\n", "display(Markdown(\"#### With distributed slack\"))\n", "# set slack_weight of the relevant elements\n", "net.ext_grid['slack_weight'] = 1\n", "net.gen['slack_weight'] = 0\n", "\n", "pp.runpp(net, distributed_slack=True)\n", "\n", "print_powers(net)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, the results of the calculation with distributed slack are equivalent to the results of the load flow calculation without distributed slack." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Second example: equal slack weights for all elements" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Without distributed slack" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Consumption of loads:\t\t\t 90.00 MW\t 100.00 MW\t 125.00 MW\t (315.00 MW total)\n", "Injection of generators (input):\t 163.00 MW\t 85.00 MW\t\t\t (248.00 MW total)\n", "Injection of generators (results):\t 163.00 MW\t 85.00 MW\t\t\t (248.00 MW total)\n", "Injection of generators (difference):\t 0.00 MW\t 0.00 MW\t\t\t ( 0.00 MW total)\n", "Slack power at ext_grid (results):\t 71.95 MW\n", "Line losses (results):\t\t\t 4.95 MW\n" ] }, { "data": { "text/markdown": [ "#### With distributed slack" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Consumption of loads:\t\t\t 90.00 MW\t 100.00 MW\t 125.00 MW\t (315.00 MW total)\n", "Injection of generators (input):\t 163.00 MW\t 85.00 MW\t\t\t (248.00 MW total)\n", "Injection of generators (results):\t 187.93 MW\t 109.93 MW\t\t\t (297.86 MW total)\n", "Injection of generators (difference):\t 24.93 MW\t 24.93 MW\t\t\t ( 49.86 MW total)\n", "Slack power at ext_grid (results):\t 24.93 MW\n", "Line losses (results):\t\t\t 7.78 MW\n" ] } ], "source": [ "display(Markdown(\"#### Without distributed slack\"))\n", "pp.runpp(net)\n", "\n", "print_powers(net)\n", "\n", "display(Markdown(\"#### With distributed slack\"))\n", "net.ext_grid['slack_weight'] = 1\n", "net.gen['slack_weight'] = 1\n", "\n", "pp.runpp(net, distributed_slack=True)\n", "\n", "print_powers(net)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sanity check\n", "\n", "In this case, the slack power is equally distributed among the ext_grid and gen elements. The power mismatch can be calculated by subtracting the consumption and line losses from the setpoint for injection: \n", "\n", "$$248 MW - 315 MW - 7.78 MW = -74.78 MW$$\n", "\n", "The power mismatch is negative, which means that $74.78 MW$ are missing for the active power to be balanced. This amount is added to the distributed slack elements ext_grid and gen according to their slack weights, resulting in the difference to the setpoints of $24.93 MW$ each (ext_grid is assumed to have a setpoint of 0)\n", "\n", "The results can be further checked by using the following calculation:\n", "$$P_{\\text{dist_slack}}=\\left(P_{\\text{res_ext_grid}}-P_{\\text{ext_grid}}\\right)+\\left(P_{\\text{res_gen1}}-P_{\\text{gen1}}\\right) + \\left(P_{\\text{res_gen2}}-P_{\\text{gen2}}\\right))$$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Power mismatch (results):\t 74.78\n", "Adjustment per element:\t\t 24.93\n", "Line losses:\t\t\t 7.78\n" ] } ], "source": [ "p_dist_slack = (net.res_ext_grid.p_mw.sum() - 0) + (net.res_gen.p_mw.sum() - net.gen.p_mw.sum())\n", "Delta_p = p_dist_slack * 1/3\n", "print(f\"Power mismatch (results):\\t{p_dist_slack:6.2f}\" + \"\\n\" +\n", " f\"Adjustment per element:\\t\\t{Delta_p:6.2f}\" + \"\\n\" +\n", " f\"Line losses:\\t\\t\\t{net.res_line.pl_mw.sum():6.2f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, the difference in active power production by the 3 power sources is as follows: $$\\varDelta P\\approx 74.78~MW\\cdot \\frac{1}{3}\\approx 24.93~MW$$\n", "Each power source must increase its active power injection by approximately $24.93~MW$ to compensate for the losses of the grid ($\\approx$ $7.78 MW$) and the unbalanced dispatch ($P_{\\text{ext_grid}}+P_{\\text{gen1}}+P_{\\text{gen2}} - \\sum P_\\text{load} = -67 MW$)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Third example: unequal slack weights" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Without distributed slack" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Consumption of loads:\t\t\t 90.00 MW\t 100.00 MW\t 125.00 MW\t (315.00 MW total)\n", "Injection of generators (input):\t 163.00 MW\t 85.00 MW\t\t\t (248.00 MW total)\n", "Injection of generators (results):\t 163.00 MW\t 85.00 MW\t\t\t (248.00 MW total)\n", "Injection of generators (difference):\t 0.00 MW\t 0.00 MW\t\t\t ( 0.00 MW total)\n", "Slack power at ext_grid (results):\t 71.95 MW\n", "Line losses (results):\t\t\t 4.95 MW\n" ] }, { "data": { "text/markdown": [ "#### With distributed slack" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Consumption of loads:\t\t\t 90.00 MW\t 100.00 MW\t 125.00 MW\t (315.00 MW total)\n", "Injection of generators (input):\t 163.00 MW\t 85.00 MW\t\t\t (248.00 MW total)\n", "Injection of generators (results):\t 181.48 MW\t 103.48 MW\t\t\t (284.96 MW total)\n", "Injection of generators (difference):\t 18.48 MW\t 18.48 MW\t\t\t ( 36.96 MW total)\n", "Slack power at ext_grid (results):\t 36.96 MW\n", "Line losses (results):\t\t\t 6.93 MW\n" ] } ], "source": [ "display(Markdown(\"#### Without distributed slack\"))\n", "gen_disp_mw = deepcopy(net.gen.p_mw.sum())\n", "\n", "pp.runpp(net)\n", "\n", "print_powers(net)\n", "\n", "display(Markdown(\"#### With distributed slack\"))\n", "\n", "net.ext_grid['slack_weight'] = 6\n", "net.gen['slack_weight'] = 3\n", "\n", "pp.runpp(net, distributed_slack=True)\n", "\n", "print_powers(net)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sanity check" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "Power mismatch (setpoint): $67.00~MW$, line losses: $6.93~MW$, total: $73.93~MW$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "Power mismatch (results): $73.93~MW$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "$\\varDelta P_{ext_grid}= P_{\\text{dist_slack}} \\cdot \\frac{6}{6+3+3}=36.96~MW$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "$\\varDelta P_{gen}= P_{\\text{dist_slack}} \\cdot \\frac{3}{6+3+3}=18.48~MW$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "$\\varDelta P = 1 * \\varDelta P_{ext_grid} + 2 * \\varDelta P_{gen}=73.93~MW$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p_mismatch = net.gen.p_mw.sum() - net.load.p_mw.sum() \n", "pl_mw = net.res_line.pl_mw.sum()\n", "p_dist_slack = (net.res_ext_grid.p_mw.sum() - 0) + (net.res_gen.p_mw.sum() - net.gen.p_mw.sum()) \n", "display(Markdown(f\"Power mismatch (setpoint): ${abs(p_mismatch):.2f}~MW$, line losses: ${pl_mw:.2f}~MW$, total: ${abs(p_mismatch)+pl_mw:.2f}~MW$\"))\n", "display(Markdown(f\"Power mismatch (results): ${p_dist_slack:.2f}~MW$\"))\n", "Delta_p_6_12 = p_dist_slack * 6/12\n", "Delta_p_3_12 = p_dist_slack * 3/12\n", "display(Markdown(\"$\\\\varDelta P_{ext_grid}= P_{\\\\text{dist_slack}} \\\\cdot \\\\frac{6}{6+3+3}=%.2f~MW$\" % Delta_p_6_12))\n", "display(Markdown(\"$\\\\varDelta P_{gen}= P_{\\\\text{dist_slack}} \\\\cdot \\\\frac{3}{6+3+3}=%.2f~MW$\" % Delta_p_3_12))\n", "display(Markdown(\"$\\\\varDelta P = 1 * \\\\varDelta P_{ext_grid} + 2 * \\\\varDelta P_{gen}=%.2f~MW$\" % p_dist_slack))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 2 }