To understand the relationship between geomagnetic storms and substorms, we examine the correlation between dispersionless proton injections observed by geosynchronous satellites and the Dst index during geomagnetic storms. It is not possible to deduce the amount of the total energy injection into the inner magnetosphere from measurements only by one or two satellites. Nonetheless, we may obtain a quantity that is proportional to the true injection rate during magnetic storms by estimating the flux increase expressed in terms of the flux ratio (fmax/fpre_ave) and the number of injections, where fpre_ave and fmax represent the average flux of prestorm level and onset level, respectively. Thus we propose to introduce a parameter, total energy injection parameter (TEIP), defined by the product of the flux ratio and the number of injections, as an indicator of the energy injected into the inner magnetosphere. Several interesting points are noted, particularly for the main phase of storms. First, the number of particle injections tends to increase with the storm size. Second, the flux ratio (fmax/fpre_ave) also tends to increase with the storm size. Third, there is also a significantly high correlation between TEIP and Dstmin. In particular, the correlation coefficients are very high, above 0.85, for those channels of energy, 50--400 keV, which represent the typical energy range of ring current particles. These results indicate that the substorm expansion activity is higher during the main phase than the recovery phase, suggesting that the substorm expansion activity seems to be closely associated with the development of magnetic storms.