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A power source apparatus mounted to a vehicle is equipped with a lead-acid battery and a lithium battery. An open circuit voltage and an internal resistance of each of the batteries are determined to satisfy the following conditions (a1), (a2), and (a3): (a1) In the use range of SOC of the lead-acid

A power source apparatus mounted to a vehicle is equipped with a lead-acid battery and a lithium battery. An open circuit voltage and an internal resistance of each of the batteries are determined to satisfy the following conditions (a1), (a2), and (a3): (a1) In the use range of SOC of the lead-acid battery and the use range of SOC of the lithium battery, there is an equal voltage point Vds at which the open circuit voltage V0 (Pb) of the lead-acid battery becomes equal to the open circuit voltage V0 (Li) of the lithium battery; (a2) The relationship of V0 (Li)V0 (Pb) is satisfied in the upper limit side of the use range of SOC of the battery; and (a3) A terminal voltage Vc (Li) of the lithium battery is not more than a set voltage Vreg of a regulator when a maximum current flows in the lithium battery.

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1. A power source apparatus, which is mounted to a vehicle, comprising: an alternator;a constant voltage control section configured to maintain a voltage of electric power generated by the alternator at a set voltage;a lead-acid battery electrically connected to the alternator;a secondary battery, e

1. A power source apparatus, which is mounted to a vehicle, comprising: an alternator;a constant voltage control section configured to maintain a voltage of electric power generated by the alternator at a set voltage;a lead-acid battery electrically connected to the alternator;a secondary battery, electrically connected in parallel to the lead-acid battery, having an energy density which is higher than an energy density of the lead-acid battery, the secondary battery being a non-aqueous electrolyte type composed of positive electrode active material and negative electrode active material, the positive electrode active material being made of lithium metal composite oxide, and the negative electrode active material being made of one selected from lithium titanium oxide, carbon, graphite, alloy containing silicon, and alloy containing tin;a protection control section configured to protect the secondary battery from overcharge by controlling a charging capacity into the secondary battery and to protect the secondary battery from over discharge by controlling a discharging capacity from the secondary battery so that a residual capacity of the secondary battery becomes within a range of 10% to 90% of a state of charge (SOC) of the secondary battery, and the protection control section outputs to the constant voltage control section an instruction signal which instructs the constant voltage control section to reduce the set voltage in order to control the charging capacity to the secondary battery; andan open and close section, arranged between the lead-acid battery and the secondary battery, configured to electrically disconnect the secondary battery from a starter motor mounted on the vehicle in order to prevent a voltage drop of the secondary battery during an engine restart of the vehicle, and an electrical load requiring a constant voltage is electrically connected to the open and close section at the side of the secondary battery,wherein an open circuit voltage and an internal resistance of the lead-acid battery and an open circuit voltage and an internal resistance of the secondary battery are determined in order to satisfy the following conditions (a), (b), and (c): (a) an equal voltage point, at which the open circuit voltage of the lead-acid battery becomes equal to the open circuit voltage of the secondary battery, is present within a range of 88% to 100% of a state of charge (SOC) of the lead-acid battery and within the range of 10% to 90% of the SOC of the secondary battery;(b) the open circuit voltage of the secondary battery is higher than the open circuit voltage of the lead-acid battery at an upper limit side from the equal voltage point within the range of 10% to 90% of the SOC of the secondary battery; and(c) a terminal voltage of the secondary battery when a maximum charging current flows in the secondary battery is not more than the set voltage which is set by the constant voltage control section, andwherein, when the engine restarts, the protection control section instructs the open and close section to disconnect the starter motor from the secondary battery and the electrical load in order to stably supply the constant voltage to the electrical load. 2. The power source apparatus according to claim 1, further comprising voltage drop suppression section configured to suppress discharge from the secondary battery to a starter motor mounted to the vehicle in order to suppress a voltage drop of the secondary battery. 3. The power source apparatus according to claim 2, wherein the protection control section further protects the secondary battery from over discharge by limiting a discharging capacity of the secondary battery so that the residual capacity of the secondary battery is within the range of the SOC of the secondary battery, wherein the protection control section limits the charging capacity to the secondary battery or the discharging capacity from the secondary battery by using the voltage drop suppression section. 4. The power source apparatus according to claim 2, wherein the voltage drop suppression section is a switch means to open and close an electric connection between the secondary battery and the starter motor, and a switch section opens the electric connection between the secondary battery and the starter motor when the lead-acid battery supplies the electric capacity to the starter motor. 5. The power source apparatus according to claim 4, wherein the switch section is one of a manual switch, an electromagnetic relay, and a semiconductor switch. 6. A power source apparatus, which is mounted to a vehicle, comprising: an alternator;a constant voltage control section configured to adjust a voltage of electric power generated by the alternator to a set voltage;a lead-acid battery electrically connected to the alternator;a secondary battery, electrically connected in parallel to the lead-acid battery, having an energy density that is higher than an energy density of the lead-acid battery, the secondary battery being a non-aqueous electrolyte type composed of positive electrode active material and negative electrode active material, the positive electrode active material being made of lithium metal composite oxide, and the negative electrode active material being made of one selected from lithium titanium oxide, carbon, graphite, alloy containing silicon, and alloy containing tin;a rectifying section placed between the lead-acid battery and the secondary battery so that a forward current direction of the rectifying section becomes a direction from the lead-acid battery to the secondary battery, and the rectifying section having a barrier voltage to the current flowing in the forward direction through the rectifying section;an open and close section, connected in parallel to the rectifying section, configured to electrically connect the alternator with the secondary battery and disconnect the alternator from the secondary battery;an open and close control section configured to (i) instruct the open and close section to close the electrical connection between the alternator and the secondary battery when the secondary battery is charged with electric power generated by the alternator, and (ii) instruct the open and close section to open the electrical connection between the alternator and the secondary battery when the rectifying section performs the rectifying operation; anda protection control section configured to protect the secondary battery from overcharge by controlling a charging capacity to the secondary battery and to protect the secondary battery from over discharge by controlling a discharging capacity from the secondary battery so that a residual capacity of the secondary battery becomes within a range of 10% to 90% of a state of charge (SOC) of the secondary battery, and the protection control section outputs, to the constant voltage control section, an instruction signal which instructs the constant voltage control section to reduce the set voltage in order to control the charging capacity to the secondary battery,wherein an open circuit voltage and an internal resistance of the lead-acid battery and an open circuit voltage and an internal resistance of the secondary battery are determined in order to satisfy the following conditions (a′), (b′), and (C′): (a′) an equal voltage point, at which the open circuit voltage of the secondary battery is equal to a subtracted voltage obtained by subtracting the barrier voltage of the rectifying section from the open circuit voltage of the lead-acid battery, is present within a range of 88% to 100% of a state of charge (SOC) of the lead-acid battery and within the range of 10% to 90% of the SOC of the secondary battery;(b′) the open circuit voltage of the secondary battery is higher than the subtracted voltage of the lead-acid battery at an upper limit side from the equal voltage point within the range of 10% to 90% of the SOC of the secondary battery; and(c′) a terminal voltage of the secondary battery when a maximum charging current flows in the secondary battery is not more than the set voltage which is set by the constant voltage control section, andwherein, when an engine of the vehicle restarts, the protection control section instructs the open and close section to disconnect the starter motor from the secondary battery and the electrical load in order to stably supply the constant voltage to the electrical load. 7. The power source apparatus according to claim 6, wherein the open and close section is composed of a semiconductor switch, and the rectifying section is composed of a parasitic diode of the semiconductor switch. 8. The power source apparatus according to claim 6, wherein the open and close section is composed of an electromagnetic relay which is connected in parallel to the rectifying section.