Electricity is unique among industries. With shoes or toothpaste, increased demand gives economies of scale and tends to bring prices down. With electricity, which cannot effectively be stored on any scale, and where the cheapest sites for hydro and wind and geothermal are always built first, and the price of fossil fuels is rising, increased demand raises prices.First, economies of scale are determined by the costs of firms, not by the demand they face. Put simply if the average cost curve of a firm is declining then you have economies of scale, if it is increasing you have diseconomies of scale. Demand is not in the picture. Second, demand will enter the picture when price is determined. As demand increases the price tends, in general, to increase, not decrease. If there is a natural monopoly then price changes resulting from demand increases could be negative as costs will be decreasing. But here the regulation that the firm is under will be a big determinant in prices changes. Third, the cheapest methods of production are always built first. This is true in general, and not just for electricity. Fourth, as just noted, if there is a natural monopoly then increased demand could decrease prices. But electricity production is more likely a natural oligopoly and thus increased demand could increase prices, independently of fuel price increases. Fifth, increased fossil fuel prices will tend to increased the cost of production, and for a given level of demand this will also increase the price of electricity. If demand was however to fall enough then prices could fall, and if both demand and fuel prices increased then price would tend to rise more than they would with only one of the two increases. In other words it is supply and demand that determines price not just one of them. Last, electricity is not unique among industries in that it has large fixed (sunk) costs. There are many industries with this property.
Update: Tom M comments in a similar manner when he suggests Supply, Meet Demand.