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Vehicle-to-grid (V2G) has the potential of reducing the cost of owning and operating electric vehicles (EVs) while increasing utility system flexibility. Unidirectional V2G is a logical first step because it can be implemented on standard J1772 chargers and it does not degrade EV batteries from cycling. In this work an optimal combined bidding formulation for regulation and spinning reserves is developed to be used by aggregators. This formulation takes into account unplanned departures by EV owners during contract periods and compensates accordingly. Optional load level and price constraints are also developed. These algorithms maximize profits to the aggregator while increasing the benefits the customers and utility. Simulations over a three month period on the ERCOT system show that implementation of these algorithms can provide significant benefits to customers, utilities, and aggregators. Comparisons with bidirectional V2G show that while the benefits of unidirectional V2G are significantly lower, so are the risks.