Determining the cost of uncertainty to electric utilities in serving highly varying loads

Dynamic market behavior of autonomous network based power systems

“…This paper is taking that direction, and its starting point is the model of market dynamics which was first introduced by Alvarado in [1]. Although there is already a list of references following from [1], like for instance [2], [3], [6], none of those references is considering the novel power system characteristics introduced by having a large amount of dispersed generators. All these generators have an extensive spectrum of possible behaviors in both physical and economical layers of the power system.…”

“…The failure of (5) to stabilize the system, has been complemented by Alvarado in [2] by adding the supplementary stabilizing signal to either the suppliers or consumers. In the case that the signal is sent only to the suppliers, equation (7) becomes:…”

“…In the case of AGC, PAS or EAS, these costs are for instance caused by increased wear, required additional maintenance, operating in a non-optimal range and loss of production opportunity. For more information on possible causes and on determining the actual costs for a certain service, we refer to [1], [2]. For ancillary service A; that is considered here, we assume that those costs are linear.…”

“…Commonly, the quadratic cost function (I) and the resulting affine marginal cost function for producers MC(Pg.J (2) and marginal benefit function for consumers MB(Pd.J (3) are used for characterizing some unit i, j: 2 In (7) and (8) both producers and consumers are assumed to take the market price as an exogenous quantity, which means that they are price takers and no market power is exercised. Producers increase their generation when market prices exceed their marginal costs, and consumers increase their consumption when market prices become lower than their marginal benefit, thus achieving equilibrium where market prices equal marginal costs.…”

“…Consumption however, is the actual usage of power at the actual system frequency and voltage, and is always equal to generation (if losses in the network are neglected). Curtail assumption in the market model of Alvarado [2] is that the market price setting mechanism is given with:…”